12583 + Mcqs in Physics Page 37 McqOptions

1801.	A circuit contains an ammeter, a battery of 30V and a resistance\[40.8\Omega \] all connected in series. If the ammeter has a coil of resistance \[480\Omega \] and a shunt of 200, the reading in the ammeter will be:
A.	0.25 A
B.	2 A
C.	1 A
D.	0.5 A
Answer» E.

Discussion

1802.	A galvanometer of resistance 50 Q is connected to battery of 3V along with a resistance of 2950 Q in series. A full scale deflection of 30 divisions is obtained in the galvanometer. In order to reduce this deflection to 20 divisions, the resistance in series should be
A.	\[5050\Omega \]
B.	\[5550\Omega \]
C.	\[6050\Omega \]
D.	\[4450\Omega \]
Answer» E.

Discussion

1803.	A \[50\Omega \] resistance is connected to a battery of 5V. A galvanometer of resistance\[100\Omega \] is to be used as an ammeter to measure current through the resistance, for this a resistance\[{{r}_{s}}\]is connected to the galvanometer. Which of the following connections should be employed if the measured current is within 1% of the current without the ammeter in the circuit?
A.	\[{{r}_{s}}=0.5\Omega \] in series with the galvanometer
B.	\[{{r}_{s}}=1\Omega \] in series with galvanometer
C.	\[{{r}_{s}}=1\Omega \] in parallel with galvanometer
D.	\[{{r}_{s}}=0.5\Omega \] in parallel with the galvanometer
Answer» E.

Discussion

1804.	A moving coil galvanometer has 150 equal divisions. Its current sensitivity is 10-divisions per milliamp ere and voltage sensitivity is 2 divisions per millivolt. In order that each division reads 1 volt, the resistance in ohms needed to be connected in series with the coil will be
A.	\[{{10}^{5}}\]
B.	\[{{10}^{3}}\]
C.	9995
D.	99995
Answer» D. 99995

Discussion

1805.	Under the influence of a uniform magnetic field a charged particle is moving in a circle of radius R with constant speed v The time period of the motion
A.	depends on both R and v
B.	is independent of both R and v
C.	depends on R and not on v
D.	depends on v and not on R
Answer» C. depends on R and not on v

Discussion

1806.	A conducting loop is placed in a magnetic field of strength B perpendicular to its plane. Radius of the loop is r, current in the loop is; and linear mass density of the wire of loop is m. Speed of any transverse wave in the loop will be
A.	\[\sqrt{\frac{Bir}{m}}\]
B.	\[\sqrt{\frac{Bir}{2m}}\]
C.	\[\sqrt{\frac{2Bir}{m}}\]
D.	\[2\sqrt{\frac{Bir}{m}}\]
Answer» B. \[\sqrt{\frac{Bir}{2m}}\]

Discussion

1807.	A conducting wire bent in the form of a parabola\[{{y}^{2}}=2x\]carries a current \[i=2A\]as shown in figure. This wire is placed in a uniform magnetic field \[\overset{\to }{\mathop{B}}\,=-4\hat{k}\]tesla. The magnetic force on the wire (in newton)
A.	\[-16\hat{i}\]
B.	\[32\hat{i}\]
C.	\[-32\hat{i}\]
D.	\[16\hat{i}\]
Answer» C. \[-32\hat{i}\]

Discussion

1808.	A closed loop PQRS carrying a current is placed in a uniform magnetic field. If the magnetic forces on segment PS, SR and RQ are \[{{F}_{1}}\], \[{{F}_{2}}\] and \[{{F}_{3}}\] respectively and are in the plane of the paper and along the directions shown, the force on the segment QP is
A.	\[\sqrt{{{({{F}_{3}}-{{F}_{1}})}^{2}}-F_{2}^{2}}\]
B.	\[{{F}_{3}}+{{F}_{1}}-{{F}_{2}}\]
C.	\[{{F}_{3}}-{{F}_{1}}+{{F}_{2}}\]
D.	\[\sqrt{{{({{F}_{3}}-{{F}_{1}})}^{2}}+F_{2}^{2}}\]
Answer» E.

Discussion

1809.	The magnetic force acting on the rod ABC in the presence of external magnetic field as shown in the figure is
A.	\[BI\ell \]
B.	\[2BI\ell \]
C.	\[BI\ell \sqrt{3}\]
D.	Zero
Answer» B. \[2BI\ell \]

Discussion

1810.	A circular arc QTS is kept in an external magnetic field \[{{\overset{\to }{\mathop{B}}\,}_{0}}\] as shown in figure. The arc carries a cur- rent I. The magnetic field is directed normal and into the page. The force acting on the arc is
A.	\[2I{{B}_{0}}R\hat{k}\]
B.	\[I{{B}_{0}}R\hat{k}\]
C.	\[-2I{{B}_{0}}R\hat{k}\]
D.	\[-I{{B}_{0}}R\hat{k}\]
Answer» C. \[-2I{{B}_{0}}R\hat{k}\]

Discussion

1811.	The figure shows two infinite semi-cylindrical shells: shell-1 and shell-2. Shell-1 carries current\[{{i}_{1}}\], in inward direction normal to the plane of paper, while shell-2 carries same current\[{{i}_{1}}\], in opposite direction. A long straight conductor lying along the common axis of the shells is carrying current\[{{i}_{2}}\]in direction same as that of current in shell-1. Force per unit length on the wire is
A.	zero
B.	\[\frac{{{\mu }_{0}}{{i}_{1}}{{i}_{2}}}{2\pi r}\]
C.	\[\frac{2{{\mu }_{0}}{{i}_{1}}{{i}_{2}}}{\pi r}\]
D.	\[\frac{2{{\mu }_{0}}{{i}_{1}}{{i}_{2}}}{{{\pi }^{2}}r}\]
Answer» E.

Discussion

1812.	A closely wound solenoid of 2000 turns and area of cross-section \[1.5\times {{10}^{-4}}\,{{m}^{2}}\] carries a current of 2.0 A. It suspended through its centre and perpendicular to its length, allowing it to turn in a horizontal plane in a uniform magnetic field \[5\times {{10}^{-2}}\]tesla making an angle of \[30{}^\circ \] with the axis of the solenoid. The torque on the solenoid will be;
A.	\[3\times {{10}^{-2}}N-m\]
B.	\[3\times {{10}^{-3}}N-m\]
C.	\[1.5\times {{10}^{-3}}N-m\]
D.	\[1.5\times {{10}^{-2}}N-m\]
Answer» E.

Discussion

1813.	A current carrying loop in the form of a right angle isosceles triangle ABC is placed in a uniform magnetic field acting along AB. If the magnetic force on the arm BC is F, what is the force on the arm AC?
A.	\[-\sqrt{2}\overset{\to }{\mathop{F}}\,\]
B.	\[-\overset{\to }{\mathop{F}}\,\]
C.	\[\overset{\to }{\mathop{F}}\,\]
D.	\[\sqrt{2}\overset{\to }{\mathop{F}}\,\]
Answer» C. \[\overset{\to }{\mathop{F}}\,\]

Discussion

1814.	A circular coil ABCD carrying a current i is placed in a uniform magnetic field. If the magnetic force on the segment AB is \[\overset{\to }{\mathop{F}}\,\]the force on the remaining segment \[BCDA\] is
A.	\[\overset{\to }{\mathop{F}}\,\]
B.	\[\overset{\to }{\mathop{-F}}\,\]
C.	\[3\overset{\to }{\mathop{F}}\,\]
D.	\[-3\overset{\to }{\mathop{F}}\,\]
Answer» C. \[3\overset{\to }{\mathop{F}}\,\]

Discussion

1815.	A proton carrying 1 MeV kinetic energy is moving in a circular path of radius R in uniform magnetic field. What should be the energy of an a-particle to describe a circle of same radius in the same field?
A.	2 MeV
B.	1 MeV
C.	0.5 MeV
D.	4 MeV
Answer» C. 0.5 MeV

Discussion

1816.	A long straight wire carries a certain current and produces a magnetic field of \[2\times {{10}^{-4}}\frac{weber}{{{m}^{2}}}\]at a perpendicular distance of 5 cm from the wire. An electron situated at 5 cm from the wire moves with a velocity \[{{10}^{7}}\,m/s\] towards the wire along perpendicular to it. The force experienced by the electron will be (charge on electron\[=1.6\times {{10}^{-19}}N\])
A.	Zero
B.	\[3.2\,N\]
C.	\[3.2\,\times {{10}^{-16}}N\]
D.	\[1.6\,\times {{10}^{-16}}N\]
Answer» D. \[1.6\,\times {{10}^{-16}}N\]

Discussion

1817.	A current carrying loop is placed in the non-uniform magnetic field whose variation in space is shown in fig. Direction of magnetic field is into the plane of paper. The magnetic force experienced by the loop is
A.	non-zero
B.	zero
C.	cannot say anything
D.	None of the above
Answer» C. cannot say anything

Discussion

1818.	A square loop ABCD carrying a current i, is placed near and coplanar with a long straight conductor XY carrying a current I, the net force on the Loop will be:
A.	\[\frac{2{{\mu }_{0}}Ii}{3\pi }\]
B.	\[\frac{{{\mu }_{0}}Ii}{2\pi }\]
C.	\[\frac{2{{\mu }_{0}}IiL}{3\pi }\]
D.	\[\frac{{{\mu }_{0}}IiL}{2\pi }\]
Answer» B. \[\frac{{{\mu }_{0}}Ii}{2\pi }\]

Discussion

1819.	A conducting ring of mass 2kg and radius 0.5 m is placed ring on a smooth horizonatal plane. The ring carries a current of i\[i=4A\]. A horizontal magnetic field B = 10 T is switched on at time t = 0 as shown in fig. The initial angular acceleration of the ring will be
A.	\[40\,\pi \,rad\,{{s}^{-2}}\]
B.	\[20\,\pi \,rad\,{{s}^{-2}}\]
C.	\[5\,\pi \,rad\,{{s}^{-2}}\]
D.	\[15\,\pi \,rad\,{{s}^{-2}}\]
Answer» B. \[20\,\pi \,rad\,{{s}^{-2}}\]

Discussion

1820.	The orbital speed of electron orbiting around a nucleus in a circular orbit of radius 50 pm is\[2.2\times {{10}^{6}}\,m{{s}^{-1}}\]. Then the magnetic dipole moment of an electron is
A.	\[1.6\times {{10}^{-19}}A{{m}^{2}}\]
B.	\[5.3\times {{10}^{-21}}A{{m}^{2}}\]
C.	\[8.8\times {{10}^{-26}}A{{m}^{2}}\]
D.	\[8.8\times {{10}^{-25}}A{{m}^{2}}\]
Answer» D. \[8.8\times {{10}^{-25}}A{{m}^{2}}\]

Discussion

1821.	A current carrying conductor placed in a magnetic field experiences maximum force when angle between current and magnetic field is
A.	\[3\pi /4\]
B.	\[\pi /2\]
C.	\[\pi /4\]
D.	zero
Answer» D. zero

Discussion

1822.	An 8 cm long wire carrying a current of 10 A is placed inside a solenoid perpendicular to its axis. If the magnetic field inside the solenoid is 0.3 T, then magnetic force on the wire is
A.	0.14N
B.	0.24 N
C.	0.34 N
D.	0.44N
Answer» C. 0.34 N

Discussion

1823.	A charged particle moves insides a pipe which is bent as shown in fig. If \[R>\frac{mv}{qB}\], then force exerted by the pipe on charged particle at P is (Neglect gravity)
A.	toward center
B.	away from center
C.	zero
D.	none of these
Answer» B. away from center

Discussion

1824.	A square current carrying loop is suspended in a uniform magnetic field acting in the plane of the loop. If the force on one arm of the loop is \[\overset{\to }{\mathop{F}}\,\], the net force on the remaining three arms of the loop is
A.	\[3\overset{\to }{\mathop{F}}\,\]
B.	\[-\overset{\to }{\mathop{F}}\,\]
C.	\[-3\overset{\to }{\mathop{F}}\,\]
D.	\[\overset{\to }{\mathop{F}}\,\]
Answer» C. \[-3\overset{\to }{\mathop{F}}\,\]

Discussion

1825.	Three infinitely long wires are placed equally apart on the circumference of a circle of radius a, perpendicular to its plane. Two of the wires carry current I each, in the same direction, while the third carries current 2I along the direction oppo- site to the other two. The magnitude of the magnetic indution \[\overset{\to }{\mathop{B}}\,\] at a distance r from the centre of the circle, for r > a, is
A.	0
B.	\[\frac{2{{\mu }_{0}}}{\pi }\frac{I}{r}\]
C.	\[-\frac{2{{\mu }_{0}}}{\pi }\frac{I}{r}\]
D.	\[\frac{2{{\mu }_{0}}}{\pi }\frac{Ia}{{{r}^{2}}}\]
Answer» B. \[\frac{2{{\mu }_{0}}}{\pi }\frac{I}{r}\]

Discussion

1826.	A long straight wire of radius R carries current i. The magnetic field inside the wire at distance r from its centre is expressed as:
A.	\[\left( \frac{{{\mu }_{0}}i}{\pi {{R}^{2}}} \right).r\]
B.	\[\left( \frac{2{{\mu }_{0}}i}{\pi {{R}^{2}}} \right).r\]
C.	\[\left( \frac{{{\mu }_{0}}i}{2\pi {{R}^{2}}} \right).r\]
D.	\[\left( \frac{{{\mu }_{0}}i}{2\pi R} \right).r\]
Answer» D. \[\left( \frac{{{\mu }_{0}}i}{2\pi R} \right).r\]

Discussion

1827.	Two equal electric currents are flowing perpendicular to each other as shown in the figure. AB and CD are perpendicular to each other and symmetrically placed with respect to the current flow. Where do we expect the resultant magnetic field to be zero?
A.	on AB
B.	on CD
C.	on both AB and CD
D.	on both OD and BO
Answer» B. on CD

Discussion

1828.	A current I flows in the anticlockwise direction through a square loop of side a lying in the XOY plane with its center at the origin. The magnetic induction at the center of the square loop is
A.	\[\frac{2\sqrt{2}{{\mu }_{0}}I}{\pi a}{{\hat{e}}_{x}}\]
B.	\[\frac{2\sqrt{2}{{\mu }_{0}}I}{\pi a}{{\hat{e}}_{z}}\]
C.	\[\frac{2\sqrt{2}{{\mu }_{0}}I}{\pi {{a}^{2}}}{{\hat{e}}_{z}}\]
D.	\[\frac{2\sqrt{2}{{\mu }_{0}}I}{\pi {{a}^{2}}}{{\hat{e}}_{x}}\]
Answer» C. \[\frac{2\sqrt{2}{{\mu }_{0}}I}{\pi {{a}^{2}}}{{\hat{e}}_{z}}\]

Discussion

1829.	A coaxial cable consists of a thin inner conductor fixed along the axis of a hollow outer conductor. The two conductors carry equal currents in opposites directions. Let \[{{B}_{1}}\]and \[{{B}_{2}}\] be the magnetic fields in the region between the conductors and outside the conductor, respectively Then,
A.	\[{{B}_{1}}\ne 0,\,{{B}_{2}}\ne 0\]
B.	\[{{B}_{1}}={{B}_{2}}=0\]
C.	\[{{B}_{1}}\ne 0,{{B}_{2}}=0\]
D.	\[{{B}_{1}}=0,{{B}_{2}}\ne 0\]
Answer» D. \[{{B}_{1}}=0,{{B}_{2}}\ne 0\]

Discussion

1830.	A steady current is flowing in a circular coil of radius R, made up of a thin conducting wire. The magnetic field at the center of the loop is\[{{B}_{L}}\]. Now, a circular loop of radius R/n is made form the same wire without changing its length, by unfolding and refolding the loop, and the same current is passed through it. If new magnetic field at the center of the coil is \[{{B}_{C}}\], then the ratio \[{{B}_{L}}/{{B}_{C}}\] is
A.	\[1:{{n}^{2}}\]
B.	\[{{n}^{1/2}}\]
C.	\[n:1\]
D.	None of these
Answer» B. \[{{n}^{1/2}}\]

Discussion

1831.	The magnetic field at point 'C' due to current flowing in 'M' shape figure is
A.	\[\frac{{{\mu }_{0}}}{2\pi }.\frac{\sqrt{3}i}{\ell }\]
B.	\[\frac{{{\mu }_{0}}}{\pi }.\frac{i}{\ell }\sqrt{3}\]
C.	zero
D.	\[\frac{{{\mu }_{0}}}{4\pi }.\frac{i}{\ell \sqrt{3}}\]
Answer» C. zero

Discussion

1832.	Two identical long conducting wires AOB and COD are placed at right angle to each other, with one above other such that 'O' is their common point for the two. The wires carry\[{{I}_{1}}\]and \[{{I}_{2}}\] currents respectively. Point T' is lying at distance 'd' from 'O' along a direction perpendicular to the plane containing the wires. The magnetic field at the point 'P' will be:
A.	\[\frac{{{\mu }_{0}}}{2\pi d}\left( \frac{{{I}_{1}}}{{{I}_{2}}} \right)\]
B.	\[\frac{{{\mu }_{0}}}{2\pi d}\left( {{I}_{1}}+{{I}_{2}} \right)\]
C.	\[\frac{{{\mu }_{0}}}{2\pi d}\left( I_{1}^{2}-I_{2}^{2} \right)\]
D.	\[\frac{{{\mu }_{0}}}{2\pi d}{{\left( I_{1}^{2}\times I_{2}^{2} \right)}^{1/2}}\]
Answer» E.

Discussion

1833.	A thin rod is bent in the shape of a small circle of radius r. If the charge per unit length of the rod is a, and if the circle is rotated about its axis at a rate of n rotations per second, the magnetic induction at a point on the axis at a large distance y from the centre
A.	\[{{\mu }_{0}}\pi {{r}^{3}}n\frac{\sigma }{{{y}^{3}}}\]
B.	\[2{{\mu }_{0}}\pi {{r}^{3}}n\frac{\sigma }{{{y}^{3}}}\]
C.	\[\left( \frac{{{\mu }_{0}}}{4\pi } \right){{r}^{3}}n\frac{\sigma }{{{y}^{3}}}\]
D.	\[\left( \frac{{{\mu }_{0}}}{2\pi } \right){{r}^{3}}n\frac{\sigma }{{{y}^{3}}}\]
Answer» B. \[2{{\mu }_{0}}\pi {{r}^{3}}n\frac{\sigma }{{{y}^{3}}}\]

Discussion

1834.	Five very long, straight insulated wires are closely bound together to form a small cable. Currents carried by the wires are: \[{{I}_{1}}=20\,A\], \[{{I}_{2}}=-6A\], \[{{I}_{3}}=12A\], \[{{I}_{4}}=-7A\], \[{{I}_{5}}=18A\]. (Negative currents are opposite in direction to the positive). The magnetic field induction at a distance of 10 cm from the cable is
A.	\[5\mu T\]
B.	\[15\mu T\]
C.	\[74\mu T\]
D.	\[128\mu T\]
Answer» D. \[128\mu T\]

Discussion

1835.	The magnetic field at O due to current in the infinite wire forming a loop as shown in Fig. is
A.	\[\frac{{{\mu }_{0}}I}{2\pi d}(\cos {{\phi }_{1}}+\cos {{\phi }_{2}})\]
B.	\[\frac{{{\mu }_{0}}I2I}{4\pi d}(tan{{\theta }_{1}}+\tan {{\theta }_{2}})\]
C.	\[\frac{{{\mu }_{0}}I}{4\pi d}(sin{{\phi }_{1}}+\sin {{\phi }_{2}})\]
D.	\[\frac{{{\mu }_{0}}I}{4\pi d}(cos{{\theta }_{1}}+\sin {{\theta }_{2}})\]
Answer» B. \[\frac{{{\mu }_{0}}I2I}{4\pi d}(tan{{\theta }_{1}}+\tan {{\theta }_{2}})\]

Discussion

1836.	A current I flows through a thin wire shaped as regular polygon of n sides which can be inscribed in a circle of radius R. The magnetic field induction at the center of polygon due to one side of the polygon is
A.	\[\frac{{{\mu }_{0}}I}{\pi R}\left( \tan \frac{\pi }{n} \right)\]
B.	\[\frac{{{\mu }_{0}}I}{4\pi R}\left( \tan \frac{\pi }{n} \right)\]
C.	\[\frac{{{\mu }_{0}}I}{2\pi R}\left( \tan \frac{\pi }{n} \right)\]
D.	\[\frac{{{\mu }_{0}}I}{2\pi R}\left( \cos \frac{\pi }{n} \right)\]
Answer» D. \[\frac{{{\mu }_{0}}I}{2\pi R}\left( \cos \frac{\pi }{n} \right)\]

Discussion

1837.	A current loop consists of two identical semicircular parts each of radius R, one lying in the x-y plane and the other in x-z plane. If the current in the loop is i, the resultant magnetic field due to the two semicircular parts at their common centre is
A.	\[\frac{{{\mu }_{0}}i}{\sqrt{2}R}\]
B.	\[\frac{{{\mu }_{0}}i}{2\sqrt{2}R}\]
C.	\[\frac{{{\mu }_{0}}i}{2R}\]
D.	\[\frac{{{\mu }_{0}}i}{4R}\]
Answer» C. \[\frac{{{\mu }_{0}}i}{2R}\]

Discussion

1838.	In the loops shown in figure, all curved sections are either semi-circles or quarter circles. All the loops carry same current. The magnetic fields at the centres have magnitudes\[{{B}_{1}}\], \[{{B}_{2}}\], \[{{B}_{3}}\], and\[{{B}_{4}}\] Then, which is correct?
A.	\[{{B}_{1}}>{{B}_{2}}>{{B}_{3}}>{{B}_{4}}\]
B.	\[{{B}_{3}}>{{B}_{4}}>{{B}_{1}}>{{B}_{1}}\]
C.	\[{{B}_{4}}>{{B}_{1}}>{{B}_{2}}>{{B}_{3}}\]
D.	\[{{B}_{1}}>{{B}_{4}}>{{B}_{3}}>{{B}_{2}}\]
Answer» D. \[{{B}_{1}}>{{B}_{4}}>{{B}_{3}}>{{B}_{2}}\]

Discussion

1839.	In the figure shown a coil of single turn is wound on a sphere of radius R and mass M. The plane of the coil is parallel to the plane and lies in the equatorial plane of the sphere. Current in the coil is i. The value of B if the sphere is in equilibrium is
A.	\[\frac{mg\,\cos \,\theta }{\pi iR}\]
B.	\[\frac{mg\,}{\pi iR}\]
C.	\[\frac{mg\,\tan \,\theta }{\pi iR}\]
D.	\[\frac{mg\,\sin \,\theta }{\pi iR}\]
Answer» C. \[\frac{mg\,\tan \,\theta }{\pi iR}\]

Discussion

1840.	A small current element of length \[d\ell \]and carrying current is placed at (1, 1, 0) and is carrying current in \['+z'\] direction. If magnetic field at origin be B\[{{\vec{B}}_{1}}\] and at point (2, 2, 0) be \[{{\vec{B}}_{2}}\] then:
A.	\[{{\vec{B}}_{1}}={{\vec{B}}_{2}}\]
B.	\[\left. \left\| {{{\vec{B}}}_{1}} \right. \right\|=\left\| 2\left. {{{\vec{B}}}_{2}} \right\| \right.\]
C.	\[{{\vec{B}}_{1}}=-{{\vec{B}}_{2}}\]
D.	\[{{\vec{B}}_{1}}=-\,2{{\vec{B}}_{2}}\]
Answer» D. \[{{\vec{B}}_{1}}=-\,2{{\vec{B}}_{2}}\]

Discussion

1841.	Two electron beams having their velocities in the ratio 1 : 2 are subjected to identical magnetic fields acting at right angles to the direction of motion of electron beams. The ratio of deflection produced is:
A.	2 : 1
B.	1 : 2
C.	4 : 1
D.	0.0444444444444444
Answer» C. 4 : 1

Discussion

1842.	A wire carrying current I has the shape as shown in adjoining figure. Linear parts of the wire are very long and parallel to X-axis while semicircular portion of radius R is lying in Y-Z plane. Magnetic field at point 0 is:
A.	\[\overset{\to }{\mathop{B}}\,=-\frac{{{\mu }_{0}}}{4\pi }\frac{I}{R}\left( \mu \hat{i}\times 2\hat{k} \right)\]
B.	\[\overset{\to }{\mathop{B}}\,=-\frac{{{\mu }_{0}}}{4\pi }\frac{I}{R}\left( \pi \hat{i}+2\hat{k} \right)\]
C.	\[\overset{\to }{\mathop{B}}\,=\frac{{{\mu }_{0}}}{4\pi }\frac{I}{R}\left( \pi \hat{i}-2\hat{k} \right)\]
D.	\[\overset{\to }{\mathop{B}}\,=\frac{{{\mu }_{0}}}{4\pi }\frac{I}{R}\left( \pi \hat{i}+2\hat{k} \right)\]
Answer» C. \[\overset{\to }{\mathop{B}}\,=\frac{{{\mu }_{0}}}{4\pi }\frac{I}{R}\left( \pi \hat{i}-2\hat{k} \right)\]

Discussion

1843.	An electron moving in a circular orbit of radius r makes n rotations per second. The magnetic field produced at the centre has magnitude:
A.	Zero
B.	\[\frac{{{\mu }_{0}}{{n}^{2}}e}{r}\]
C.	\[\frac{{{\mu }_{0}}ne}{2r}\]
D.	\[\frac{{{\mu }_{0}}ne}{2\pi r}\]
Answer» D. \[\frac{{{\mu }_{0}}ne}{2\pi r}\]

Discussion

1844.	A long straight wire of radius a carries a steady current I. The current is uniformly distributed over its cross-section. The ratio of the magnetic fields B and B', at radial distances \[\frac{a}{2}\] and 2a respectively, from the axis of the wire is:
A.	\[\frac{1}{4}\]
B.	\[\frac{1}{2}\]
C.	1
D.	4
Answer» D. 4

Discussion

1845.	Two wires are wrapped over a wooden cylinder to form two coaxial loops a carrying current\[{{i}_{1}}\] and\[{{i}_{2}}\]. If \[{{i}_{2}}=8{{i}_{1}}\] the value of x for B = 0 at the origin O is:
A.	\[\sqrt{(\sqrt{7}}-1)R\]
B.	\[\sqrt{5}R\]
C.	\[\sqrt{3}R\]
D.	\[\sqrt{7}R\]
Answer» E.

Discussion

1846.	The current density \[\vec{j}\] inside a long, solid, cylindrical wire of radius a=12 mm is in the direction of the central axis, and its magnitude varies linearly with radial distance r from the axis according to\[J=\frac{{{J}_{0}}r}{a}\], where \[{{J}_{0}}=\frac{{{10}^{5}}}{4\pi }A/{{m}^{2}}.\] Find the magnitude of the magnetic field at in\[\mu T\]
A.	\[10\mu T\]
B.	\[4\mu T\]
C.	\[5\mu T\]
D.	\[3\mu T\]
Answer» B. \[4\mu T\]

Discussion

1847.	Consider two thin identical conducting wires covered with very thin insulating material. One of the wires is bent into a loop and produces magnetic field\[{{B}_{1}}\], at its centre when a current I passes through it. The ratio \[{{B}_{1}}:{{B}_{2}}\] is:
A.	1 : 1
B.	1 : 3
C.	0.0479166666666667
D.	0.375694444444444
Answer» C. 0.0479166666666667

Discussion

1848.	Two long parallel wires P and Q are both perpendicular to the plane of the paper with distance of 5m between them. If P and Q carry currents of 2.5 amp and 5 amp respectively in the same direction, then the magnetic field at a point half-way between the wires is
A.	\[\frac{3{{\mu }_{0}}}{2\pi }\]
B.	\[\frac{{{\mu }_{0}}}{\pi }\]
C.	\[\frac{\sqrt{3}{{\mu }_{0}}}{2\pi }\]
D.	\[\frac{{{\mu }_{0}}}{2\pi }\]
Answer» E.

Discussion

1849.	If the magnetic field at P can be written as K tan \[\left( \frac{\alpha }{2} \right)\], then K
A.	\[\frac{{{\mu }_{0}}I}{4\pi d}\]
B.	\[\frac{{{\mu }_{0}}I}{2\pi d}\]
C.	\[\frac{{{\mu }_{0}}I}{\pi d}\]
D.	\[\frac{2{{\mu }_{0}}I}{\pi d}\]
Answer» C. \[\frac{{{\mu }_{0}}I}{\pi d}\]

Discussion

1850.	The magnetic field due to a current carrying circular loop of radius 3 cm at a point on the axis at a distance of 4 cm from the centre is \[54\,\mu T\]. What will be its value at the centre of loop?
A.	\[125\mu T\]
B.	\[150\mu T\]
C.	\[250\mu T\]
D.	\[75\mu T\]
Answer» D. \[75\mu T\]

Discussion

Explore topic-wise MCQs in Joint Entrance Exam - Main (JEE Main).

A circuit contains an ammeter, a battery of 30V and a resistance\[40.8\Omega \] all connected in series. If the ammeter has a coil of resistance \[480\Omega \] and a shunt of 200, the reading in the ammeter will be:

A galvanometer of resistance 50 Q is connected to battery of 3V along with a resistance of 2950 Q in series. A full scale deflection of 30 divisions is obtained in the galvanometer. In order to reduce this deflection to 20 divisions, the resistance in series should be

A moving coil galvanometer has 150 equal divisions. Its current sensitivity is 10-divisions per milliamp ere and voltage sensitivity is 2 divisions per millivolt. In order that each division reads 1 volt, the resistance in ohms needed to be connected in series with the coil will be

Under the influence of a uniform magnetic field a charged particle is moving in a circle of radius R with constant speed v The time period of the motion

A conducting loop is placed in a magnetic field of strength B perpendicular to its plane. Radius of the loop is r, current in the loop is; and linear mass density of the wire of loop is m. Speed of any transverse wave in the loop will be

A conducting wire bent in the form of a parabola\[{{y}^{2}}=2x\]carries a current \[i=2A\]as shown in figure. This wire is placed in a uniform magnetic field \[\overset{\to }{\mathop{B}}\,=-4\hat{k}\]tesla. The magnetic force on the wire (in newton)

A closed loop PQRS carrying a current is placed in a uniform magnetic field. If the magnetic forces on segment PS, SR and RQ are \[{{F}_{1}}\], \[{{F}_{2}}\] and \[{{F}_{3}}\] respectively and are in the plane of the paper and along the directions shown, the force on the segment QP is

The magnetic force acting on the rod ABC in the presence of external magnetic field as shown in the figure is

A circular arc QTS is kept in an external magnetic field \[{{\overset{\to }{\mathop{B}}\,}_{0}}\] as shown in figure. The arc carries a cur- rent I. The magnetic field is directed normal and into the page. The force acting on the arc is

A current carrying loop in the form of a right angle isosceles triangle ABC is placed in a uniform magnetic field acting along AB. If the magnetic force on the arm BC is F, what is the force on the arm AC?

A circular coil ABCD carrying a current i is placed in a uniform magnetic field. If the magnetic force on the segment AB is \[\overset{\to }{\mathop{F}}\,\]the force on the remaining segment \[BCDA\] is

A proton carrying 1 MeV kinetic energy is moving in a circular path of radius R in uniform magnetic field. What should be the energy of an a-particle to describe a circle of same radius in the same field?

A current carrying loop is placed in the non-uniform magnetic field whose variation in space is shown in fig. Direction of magnetic field is into the plane of paper. The magnetic force experienced by the loop is

A square loop ABCD carrying a current i, is placed near and coplanar with a long straight conductor XY carrying a current I, the net force on the Loop will be:

A conducting ring of mass 2kg and radius 0.5 m is placed ring on a smooth horizonatal plane. The ring carries a current of i\[i=4A\]. A horizontal magnetic field B = 10 T is switched on at time t = 0 as shown in fig. The initial angular acceleration of the ring will be

The orbital speed of electron orbiting around a nucleus in a circular orbit of radius 50 pm is\[2.2\times {{10}^{6}}\,m{{s}^{-1}}\]. Then the magnetic dipole moment of an electron is

A current carrying conductor placed in a magnetic field experiences maximum force when angle between current and magnetic field is

An 8 cm long wire carrying a current of 10 A is placed inside a solenoid perpendicular to its axis. If the magnetic field inside the solenoid is 0.3 T, then magnetic force on the wire is

A charged particle moves insides a pipe which is bent as shown in fig. If \[R>\frac{mv}{qB}\], then force exerted by the pipe on charged particle at P is (Neglect gravity)

A square current carrying loop is suspended in a uniform magnetic field acting in the plane of the loop. If the force on one arm of the loop is \[\overset{\to }{\mathop{F}}\,\], the net force on the remaining three arms of the loop is

A long straight wire of radius R carries current i. The magnetic field inside the wire at distance r from its centre is expressed as:

Two equal electric currents are flowing perpendicular to each other as shown in the figure. AB and CD are perpendicular to each other and symmetrically placed with respect to the current flow. Where do we expect the resultant magnetic field to be zero?

A current I flows in the anticlockwise direction through a square loop of side a lying in the XOY plane with its center at the origin. The magnetic induction at the center of the square loop is

The magnetic field at point 'C' due to current flowing in 'M' shape figure is

A thin rod is bent in the shape of a small circle of radius r. If the charge per unit length of the rod is a, and if the circle is rotated about its axis at a rate of n rotations per second, the magnetic induction at a point on the axis at a large distance y from the centre

The magnetic field at O due to current in the infinite wire forming a loop as shown in Fig. is

A current I flows through a thin wire shaped as regular polygon of n sides which can be inscribed in a circle of radius R. The magnetic field induction at the center of polygon due to one side of the polygon is

A current loop consists of two identical semicircular parts each of radius R, one lying in the x-y plane and the other in x-z plane. If the current in the loop is i, the resultant magnetic field due to the two semicircular parts at their common centre is

In the loops shown in figure, all curved sections are either semi-circles or quarter circles. All the loops carry same current. The magnetic fields at the centres have magnitudes\[{{B}_{1}}\], \[{{B}_{2}}\], \[{{B}_{3}}\], and\[{{B}_{4}}\] Then, which is correct?

In the figure shown a coil of single turn is wound on a sphere of radius R and mass M. The plane of the coil is parallel to the plane and lies in the equatorial plane of the sphere. Current in the coil is i. The value of B if the sphere is in equilibrium is

A small current element of length \[d\ell \]and carrying current is placed at (1, 1, 0) and is carrying current in \['+z'\] direction. If magnetic field at origin be B\[{{\vec{B}}_{1}}\] and at point (2, 2, 0) be \[{{\vec{B}}_{2}}\] then:

Two electron beams having their velocities in the ratio 1 : 2 are subjected to identical magnetic fields acting at right angles to the direction of motion of electron beams. The ratio of deflection produced is:

A wire carrying current I has the shape as shown in adjoining figure. Linear parts of the wire are very long and parallel to X-axis while semicircular portion of radius R is lying in Y-Z plane. Magnetic field at point 0 is:

An electron moving in a circular orbit of radius r makes n rotations per second. The magnetic field produced at the centre has magnitude:

A long straight wire of radius a carries a steady current I. The current is uniformly distributed over its cross-section. The ratio of the magnetic fields B and B', at radial distances \[\frac{a}{2}\] and 2a respectively, from the axis of the wire is:

Two wires are wrapped over a wooden cylinder to form two coaxial loops a carrying current\[{{i}_{1}}\] and\[{{i}_{2}}\]. If \[{{i}_{2}}=8{{i}_{1}}\] the value of x for B = 0 at the origin O is:

Consider two thin identical conducting wires covered with very thin insulating material. One of the wires is bent into a loop and produces magnetic field\[{{B}_{1}}\], at its centre when a current I passes through it. The ratio \[{{B}_{1}}:{{B}_{2}}\] is:

Two long parallel wires P and Q are both perpendicular to the plane of the paper with distance of 5m between them. If P and Q carry currents of 2.5 amp and 5 amp respectively in the same direction, then the magnetic field at a point half-way between the wires is

If the magnetic field at P can be written as K tan \[\left( \frac{\alpha }{2} \right)\], then K

The magnetic field due to a current carrying circular loop of radius 3 cm at a point on the axis at a distance of 4 cm from the centre is \[54\,\mu T\]. What will be its value at the centre of loop?