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MCQOPTIONS
This section includes 12583 Mcqs, each offering curated multiple-choice questions to sharpen your Joint Entrance Exam - Main (JEE Main) knowledge and support exam preparation. Choose a topic below to get started.
| 2501. |
A parallel plate capacitor with air between the plates has a capacitance of 8 pF. Calculate the capacitance if the distance between the plates is reduced by half and the space between them is filled with a substance of dielectric constant. \[\left( {{\varepsilon }_{r}}=6 \right)\] |
| A. | 72 pF |
| B. | 81 pF |
| C. | 84 pF |
| D. | 96 PF |
| Answer» E. | |
| 2502. |
The capacitor, whose capacitance is 6, 6 and\[3\mu F\]respectively are connected in series with 20 volt line. Find the charge on \[3\mu F\]. |
| A. | \[30\mu C\] |
| B. | \[60\mu F\] |
| C. | \[15\mu F\] |
| D. | \[90\mu F\] |
| Answer» B. \[60\mu F\] | |
| 2503. |
Three condenser each of capacitance 2F are put in series. The resultant capacitance is |
| A. | 6 F |
| B. | 3/2 F |
| C. | 2/3 F |
| D. | 5 F |
| Answer» D. 5 F | |
| 2504. |
A capacitor has two circular plates whose radius are 8cm and distance between them is 1mm. When mica (dielectric constant = 6) is placed between the plates. The capacitance of this capacitor and the energy stored when it is given potential of 150 volt respectively are |
| A. | \[1.06\times {{10}^{-5}}F,1.2\times {{10}^{-9}}J\] |
| B. | \[1.068\times {{10}^{-9}}F,1.2\times {{10}^{-5}}J\] |
| C. | \[1.2\times {{10}^{-9}}F,1.068\times {{10}^{-5}}J\] |
| D. | \[1.6\times {{10}^{-9}}F,1.068\times {{10}^{-5}}J\] |
| Answer» C. \[1.2\times {{10}^{-9}}F,1.068\times {{10}^{-5}}J\] | |
| 2505. |
If earth is assumed to be a conducting sphere having radius \[R=6400km,\]it?s capacitance will be: |
| A. | \[711\mu F\] |
| B. | \[218\mu F\] |
| C. | \[16\mu F\] |
| D. | \[8\mu F\] |
| Answer» E. | |
| 2506. |
The work done in placing a charge of \[8\times {{10}^{-18}}\]coulomb on a condenser of capacity 100 microfarad is |
| A. | \[3.1\times {{10}^{-26}}joule\] |
| B. | \[4\times {{10}^{-10}}joule\] |
| C. | \[3.2\times {{10}^{-32}}joule\] |
| D. | \[16\times {{10}^{-32}}joule\] |
| Answer» D. \[16\times {{10}^{-32}}joule\] | |
| 2507. |
A parallel plate condenser is filled with two dielectrics as shown. Area of each plate is \[A{{m}^{2}}\]and the separation is t m. The dielectric constants are \[{{k}_{1}}\] and \[{{k}_{2}}\] respectively. Its capacitance in farad will be |
| A. | \[\frac{{{\varepsilon }_{0}}A}{t}\left( {{k}_{1}}+{{k}_{2}} \right)\] |
| B. | \[\frac{{{\varepsilon }_{0}}A}{t}.\frac{{{k}_{1}}+{{k}_{2}}}{2}\] |
| C. | \[\frac{2{{\varepsilon }_{0}}A}{t}\left( {{k}_{1}}+{{k}_{2}} \right)\] |
| D. | \[\frac{{{\varepsilon }_{0}}A}{t}.\frac{{{k}_{1}}-{{k}_{2}}}{2}\] |
| Answer» C. \[\frac{2{{\varepsilon }_{0}}A}{t}\left( {{k}_{1}}+{{k}_{2}} \right)\] | |
| 2508. |
Eight drops of mercury of equal radii possessing equal charges combine to form a big drop. Then the capacitance of bigger drop compared to each individual small drop is |
| A. | 8 times |
| B. | 4 times |
| C. | 2 times |
| D. | 32 times |
| Answer» D. 32 times | |
| 2509. |
Two vertical metallic plates carrying equal and opposite charges are kept parallel to each other like a parallel plate capacitor. A small spherical metallic ball is suspended by a long insulated thread such that it hangs freely in the center of the two metallic plates. The ball, which is uncharged, is taken slowly towards the positively charged plate and is made to touch and plate. Then the ball will |
| A. | stick to the positively charged plate |
| B. | come back to its original position and will remain there |
| C. | oscillate between the two plates touching each plate in turn |
| D. | oscillate between the two plates without touch them |
| Answer» D. oscillate between the two plates without touch them | |
| 2510. |
If in parallel plate capacitor, which is connected to a battery, we fill dielectrics in whole space of its plates, then which of the following increases? |
| A. | Q and V |
| B. | V and E |
| C. | E and C |
| D. | Q and C |
| Answer» E. | |
| 2511. |
On decreasing the distance between the plates of a parallel plate capacitor, its capacitance |
| A. | remains unaffected |
| B. | decreases |
| C. | first increases then decreases. |
| D. | increases |
| Answer» E. | |
| 2512. |
Each corner of a cube of side l has a negative charge, -q. The electrostatic potential energy of a charge q at the center of the cube is |
| A. | \[-\frac{4{{q}^{2}}}{\sqrt{2}\pi {{\varepsilon }_{0}}l}\] |
| B. | \[\frac{\sqrt{3}{{q}^{2}}}{4\pi {{\varepsilon }_{0}}l}\] |
| C. | \[\frac{4{{q}^{2}}}{\sqrt{2}\pi {{\varepsilon }_{0}}l}\] |
| D. | \[-\frac{4{{q}^{2}}}{\sqrt{3}\pi {{\varepsilon }_{0}}l}\] |
| Answer» E. | |
| 2513. |
Two identical thin rings each of radius R meters are coaxially placed at a distance R meters apart. If \[{{Q}_{1}}\]coulomb and \[{{Q}_{2}}\]coulomb are respectively the charges uniformly spread on the two rings, the work done in moving a charge q from the center of one ring to that of other is |
| A. | zero |
| B. | \[\frac{q\left( {{Q}_{1}}-{{Q}_{2}} \right)\left( \sqrt{2}-1 \right)}{\sqrt{2}.4\pi {{\varepsilon }_{0}}R}\] |
| C. | \[\frac{q\sqrt{2}\left( {{Q}_{1}}+{{Q}_{2}} \right)}{4\pi {{\varepsilon }_{0}}R}\] |
| D. | \[\frac{q\left( {{Q}_{1}}+{{Q}_{2}} \right)\left( \sqrt{2}+1 \right)}{\sqrt{2}.4\pi {{\varepsilon }_{0}}R}\] |
| Answer» C. \[\frac{q\sqrt{2}\left( {{Q}_{1}}+{{Q}_{2}} \right)}{4\pi {{\varepsilon }_{0}}R}\] | |
| 2514. |
Positive and negative point charges of equal magnitude are kept at (0, 0, \[\frac{a}{2}\]) and [0, 0, \[-\frac{a}{2}\] ] respectively. The work done by the electric field when another positive point charge is moved from (-a, 0, 0) to (0, a, 0) is |
| A. | positive |
| B. | negative |
| C. | zero |
| D. | depends on the path connecting the initial and final positions |
| Answer» D. depends on the path connecting the initial and final positions | |
| 2515. |
As per the diagram, a point charge +q is placed at the origin O. Work done in taking another point charge-Q from the point A [coordinates (0, a)] to another point B [coordinates (a, 0)] along the straight path AB is: |
| A. | zero |
| B. | \[\left( \frac{-qQ}{4\pi {{\varepsilon }_{0}}}\frac{1}{{{a}^{2}}} \right)\sqrt{2}a\] |
| C. | \[\left( \frac{-qQ}{4\pi {{\varepsilon }_{0}}}\frac{1}{{{a}^{2}}} \right).\frac{a}{\sqrt{2}}\] |
| D. | \[\left( \frac{qQ}{4\pi {{\varepsilon }_{0}}}\frac{1}{{{a}^{2}}} \right).\sqrt{2}a\] |
| Answer» B. \[\left( \frac{-qQ}{4\pi {{\varepsilon }_{0}}}\frac{1}{{{a}^{2}}} \right)\sqrt{2}a\] | |
| 2516. |
A ball of mass 1 g carrying a change \[{{10}^{-8}}C\]moves from a point A at potential 600 V to a point B at zero potential. The change in its K.E. |
| A. | \[-6\times {{10}^{-6}}erg\] |
| B. | \[-6\times {{10}^{-6}}J\] |
| C. | \[6\times {{10}^{-6}}J\] |
| D. | \[6\times {{10}^{-6}}erg\] |
| Answer» D. \[6\times {{10}^{-6}}erg\] | |
| 2517. |
Two points P and Q are maintained at the potentials of 10 V and -4 V, respectively. The work done in moving 100 electrons from P to Q is: |
| A. | \[9.60\times {{10}^{-17}}J\] |
| B. | \[-2.24\times {{10}^{-16}}J\] |
| C. | \[2.24\times {{10}^{-16}}J\] |
| D. | \[-9.60\times {{10}^{-17}}J\,\] |
| Answer» D. \[-9.60\times {{10}^{-17}}J\,\] | |
| 2518. |
A and B are two points in an electric field. If the work done in carrying 4.0C of electric charge from work done in moving 100 electrons from P to Q |
| A. | zero |
| B. | 2.0 V |
| C. | 4.0 V |
| D. | 16.0 V |
| Answer» D. 16.0 V | |
| 2519. |
Two conducting spheres of radii \[{{R}_{1}}\] and \[{{R}_{2}}\]having charges \[{{Q}_{1}}\] and \[{{Q}_{2}}\]respectively are connected to each other. There is |
| A. | no change in the energy of the system |
| B. | an increase in the energy of the system |
| C. | always a decrease in the energy of the system |
| D. | a decrease in the energy of the system unless \[{{Q}_{1}}{{R}_{2}}={{Q}_{2}}{{R}_{1}}\] |
| Answer» E. | |
| 2520. |
Figure shows a system of three positive charges placed at the verticals of and equilateral triangle. To decrease the potential energy of the system, |
| A. | a positive charge should be placed at centroid. |
| B. | a negative charge should be placed at centroid. |
| C. | distance between the charges should be decreased. |
| D. | it should be rotated by an angle of \[\frac{\pi }{2}\] radian. |
| Answer» D. it should be rotated by an angle of \[\frac{\pi }{2}\] radian. | |
| 2521. |
In the electric field of a point charge q, a certain charge is carried from point A to B, C, D and E. Then the work done is |
| A. | least along the path AB |
| B. | least along the path AD |
| C. | zero along all the paths AB, AC, AD and AE |
| D. | least along AE |
| Answer» D. least along AE | |
| 2522. |
The potential energy of a system of two charges is negative when |
| A. | both the charges are positive |
| B. | both the charges are negative |
| C. | one charge is positive and other is negative |
| D. | both the charges are separated by infinite distance |
| Answer» D. both the charges are separated by infinite distance | |
| 2523. |
Two concentric conducting spherical shells of radii \[{{a}_{1}}\]and \[{{a}_{2}}\]\[({{a}_{2}}>{{a}_{1}})\] are charged to potentials \[{{\phi }_{1}}\] and \[{{\phi }_{2}}\], respectively. Find the charge on the inner shell. |
| A. | \[{{q}_{1}}=4\pi {{\varepsilon }_{0}}\left( \frac{{{\phi }_{1}}-{{\phi }_{2}}}{{{a}_{2}}-{{a}_{1}}} \right){{a}_{1}}{{a}_{2}}\] |
| B. | \[{{q}_{1}}=4\pi {{\varepsilon }_{0}}\left( \frac{{{\phi }_{1}}+{{\phi }_{2}}}{{{a}_{2}}+{{a}_{1}}} \right){{a}_{1}}{{a}_{2}}\] |
| C. | \[{{q}_{1}}=4\pi {{\varepsilon }_{0}}\left( \frac{{{\phi }_{1}}-{{\phi }_{2}}}{{{a}_{2}}+{{a}_{1}}} \right){{a}_{1}}{{a}_{2}}\] |
| D. | \[{{q}_{1}}=4\pi {{\varepsilon }_{0}}\left( \frac{{{\phi }_{1}}+{{\phi }_{2}}}{{{a}_{2}}-{{a}_{1}}} \right){{a}_{1}}{{a}_{2}}\] |
| Answer» B. \[{{q}_{1}}=4\pi {{\varepsilon }_{0}}\left( \frac{{{\phi }_{1}}+{{\phi }_{2}}}{{{a}_{2}}+{{a}_{1}}} \right){{a}_{1}}{{a}_{2}}\] | |
| 2524. |
Two charges \[{{q}_{1}}\] and \[{{q}_{2}}\] are placed 30 cm apart, as shown in the figure. A third charge \[{{q}_{3}}\]is moved along the arc of a circle of radius 40 cm from C to D. The change in the potential energy of the system is \[\frac{{{q}_{3}}}{4\pi \,{{\in }_{0}}}\,k,\] where k is |
| A. | \[8{{q}_{1}}\] |
| B. | \[6{{q}_{1}}\] |
| C. | \[8{{q}_{2}}\] |
| D. | \[6{{q}_{2}}\] |
| Answer» D. \[6{{q}_{2}}\] | |
| 2525. |
An infinite non-conducting sheet has a surface charge density \[\sigma =0.1\mu C/{{m}^{2}}\]on one side. How far apart are equipotential surfaces whose potential differ by 50 volt? |
| A. | \[8.8mm\] |
| B. | \[8.8cm\] |
| C. | \[8.8\text{ }\mu rn\] |
| D. | \[8.8pm\] |
| Answer» B. \[8.8cm\] | |
| 2526. |
The electric potential at a point (x, y, z) is given by \[V=-{{x}^{2}}y-x{{z}^{3}}+4.\] The electric field E at that point is |
| A. | \[\vec{E}=\hat{i}2xy+\hat{j}({{x}^{2}}+{{y}^{2}})+\hat{k}(3xz-{{y}^{2}})\] |
| B. | \[\vec{E}=\hat{i}{{z}^{3}}+\hat{j}xyz+\hat{k}{{z}^{2}}\] |
| C. | \[\vec{E}=\hat{i}(2xy-{{z}^{3}})+\hat{j}x{{y}^{2}}+\hat{k}3{{z}^{2}}x\] |
| D. | \[\vec{E}=\hat{i}(2xy+{{z}^{3}})+\hat{j}{{x}^{2}}+\hat{k}3x{{z}^{2}}\] |
| Answer» E. | |
| 2527. |
A sphere of radius 2R has a uniform charge density \[\rho .\] The difference in the electric potential at \[r=R\], \[r=0\]from the center is |
| A. | \[\frac{-\rho {{R}^{2}}}{{{\in }_{0}}}\] |
| B. | \[\frac{-2\rho {{R}^{2}}}{{{\in }_{0}}}\] |
| C. | \[\frac{\rho {{R}^{2}}}{3{{\in }_{0}}}\] |
| D. | \[\frac{-\rho {{R}^{2}}}{6{{\in }_{0}}}\,\] |
| Answer» E. | |
| 2528. |
A charge +q fixed at each of the points \[x={{x}_{0}},x=3{{x}_{0}},x=5{{x}_{0}}....\] up to \[\infty \] on X-axis and charge -q is fixed on each of the points \[x=2{{x}_{0}},x=4{{x}_{0}},....\] up to \[\infty \]. Here \[{{x}_{0}}\] is a positive constant. Take the potential at a point due to a charge Q at a distance r form it to be \[\frac{Q}{4\pi {{\varepsilon }_{0}}r},\] then the potential at the origin due to above system of charges will be: |
| A. | zero |
| B. | infinite |
| C. | \[\frac{q}{8\,\pi \,{{\varepsilon }_{0}}{{x}_{0}}\,{{\log }_{e}}\,2}\] |
| D. | \[\frac{q\,{{\log }_{e}}\,2}{4\,\pi \,{{\varepsilon }_{0}}{{x}_{0}}}\] |
| Answer» E. | |
| 2529. |
Figure shows a system of three concentric metal shells A, B and C with radii a, 2a and 3a respectively. Shell B is earthed and shell C is given a charge Q. Now if shell C is connected to shell, A then the final charge on the shell B, is equal to |
| A. | -4Q/3 |
| B. | -8Q/11 |
| C. | -5Q/3 |
| D. | -3Q/7 |
| Answer» C. -5Q/3 | |
| 2530. |
Three identical metallic uncharged spheres A, B and C each of radius a, are kept at the corners of an equilateral triangle of side d(d>>a) as shown in Fig. The fourth sphere (of radius a), which has a charge q, touches A and is then removed to a position far away. B is earthed and then the earth connection is removed. C is then earthed. The charge on C is |
| A. | \[\frac{qa}{2d}\left( \frac{2d-a}{2d} \right)\] |
| B. | \[\frac{qa}{2d}\left( \frac{2d-a}{d} \right)\] |
| C. | \[-\frac{qa}{2d}\left( \frac{d-a}{d} \right)\] |
| D. | \[-\frac{2qa}{d}\left( \frac{d-a}{2d} \right)\] |
| Answer» D. \[-\frac{2qa}{d}\left( \frac{d-a}{2d} \right)\] | |
| 2531. |
In a region, the potential is represented by \[V\left( x,y,z \right)=6x-8xy-8y+6yz,\] where V is in volts and x, y, z are in meters. The electric force experienced by change of 2 coulomb situate at point (1, 1, 1) is: |
| A. | \[6\sqrt{5}N\] |
| B. | \[30N\] |
| C. | \[24N\] |
| D. | \[4\sqrt{3}N\] |
| Answer» E. | |
| 2532. |
A charge of 3 coulomb moving in uniform electric field experiences a force of 3000 newton. The potential difference between the two points situated in a field at a distance of 1 cm from each other will be: |
| A. | 100 |
| B. | 5000 |
| C. | 10 |
| D. | 50 |
| Answer» D. 50 | |
| 2533. |
There is a uniform electrostatic filed in a region. The potential at various points on a small sphere centered at P, in the region, is found to vary between in the limits 589.0 V to 589.8 V. What is the potential at a point on the sphere whose radius vector makes an angle of \[60{}^\circ \]with the direction of the field? |
| A. | 589.5 V |
| B. | 589.2 V |
| C. | 589.4 V |
| D. | 589.6 V |
| Answer» D. 589.6 V | |
| 2534. |
Three identical particles, each possessing the mass m and charge +q, are placed at the corners of an equilateral triangle with side \[{{r}_{0}}.\] The particles are simultaneously set free and start flying apart symmetrically due to Coulomb?s repulsion foces. The work performed by Coulomb?s forces acting on to a very large distance is \[(\text{where }k=1/4\pi {{\varepsilon }_{0}}.)\] |
| A. | \[\frac{3k{{q}^{2}}}{{{r}_{0}}}\] |
| B. | \[\frac{k{{q}^{2}}}{{{r}_{0}}}\] |
| C. | \[\frac{3k{{q}^{2}}}{2{{r}_{0}}}\] |
| D. | \[\frac{k{{q}^{2}}}{2{{r}_{0}}}\] |
| Answer» C. \[\frac{3k{{q}^{2}}}{2{{r}_{0}}}\] | |
| 2535. |
Three concentric charged metallic spherical shells A, B and C have radii a, b and c; change densities \[\sigma ,-\sigma \] and \[\sigma \] and potentials \[{{V}_{A}},{{V}_{B}}\] and \[{{V}_{C}}\] respectively. Then which of the following relations is correct? |
| A. | \[{{V}_{A}}=\left( a+b+c \right)\frac{\sigma }{{{\varepsilon }_{0}}}\] |
| B. | \[{{V}_{B}}=\left( \frac{{{a}^{2}}}{b}-b+c \right)\frac{\sigma }{{{\varepsilon }_{0}}}\] |
| C. | \[{{V}_{C}}=\left( \frac{{{a}^{2}}+{{b}^{2}}}{b}+c \right)\frac{\sigma }{{{\varepsilon }_{0}}}\] |
| D. | \[{{V}_{A}}={{V}_{B}}={{V}_{C}}=\left( a+b+c \right)\frac{\sigma }{{{\varepsilon }_{0}}}\] |
| Answer» C. \[{{V}_{C}}=\left( \frac{{{a}^{2}}+{{b}^{2}}}{b}+c \right)\frac{\sigma }{{{\varepsilon }_{0}}}\] | |
| 2536. |
An electron having charge e and mass m starts from the lower plate of two metallic plates separated by a distance d. If the potential difference between the plates is V, the time taken by the electron to reach the upper plate is given charge on C is |
| A. | \[\sqrt{\frac{2m{{d}^{2}}}{eV}}\] |
| B. | \[\sqrt{\frac{m{{d}^{2}}}{eV}}\] |
| C. | \[\sqrt{\frac{m{{d}^{2}}}{2eV}}\] |
| D. | \[\frac{2m{{d}^{2}}}{eV}\] |
| Answer» B. \[\sqrt{\frac{m{{d}^{2}}}{eV}}\] | |
| 2537. |
A charge Q is distributed over two concentric hollow spheres of radii r and R(R>r) such that the surface densities are equal. The potential at the common center is \[\frac{1}{4\pi {{\varepsilon }_{0}}}\]times- |
| A. | \[Q\left[ \frac{r+R}{{{r}^{2}}+{{R}^{2}}} \right]\] |
| B. | \[\frac{Q}{2}\left[ \frac{r+R}{{{r}^{2}}+{{R}^{2}}} \right]\] |
| C. | \[2Q\left[ \frac{r+R}{{{r}^{2}}+{{R}^{2}}} \right]\] |
| D. | zero |
| Answer» B. \[\frac{Q}{2}\left[ \frac{r+R}{{{r}^{2}}+{{R}^{2}}} \right]\] | |
| 2538. |
Four charges \[{{q}_{1}}=2\times {{10}^{-8}}C,\] \[{{q}_{2}}=-2\times {{10}^{-8}}C,\]\[{{q}_{3}}=-3\times {{10}^{-8}}C\], \[{{q}_{3}}=6\times {{10}^{-8}}C\]are placed at four corners of a square of side \[\sqrt{2}\] m. What is hollow spheres of radii r and R (R > r) such that the common center of the square? |
| A. | 270 V |
| B. | 300 V |
| C. | Zero |
| D. | 100 V |
| Answer» B. 300 V | |
| 2539. |
The electric potential at a point (x, y) in the \[x\text{ }\text{ }y\] plane is given by \[V=-kxy.\] The field intensity at a distance r from the origin varies as |
| A. | \[{{r}^{2}}\] |
| B. | \[r\] |
| C. | \[\frac{1}{r}\] |
| D. | \[\frac{1}{{{r}^{2}}}\] |
| Answer» C. \[\frac{1}{r}\] | |
| 2540. |
The expression \[E=-\frac{dv}{dr}\]implies, that electric field is in that direction in which |
| A. | increase in potential is steepest. |
| B. | decrease in potential is steepest. |
| C. | change is potential is minimum. |
| D. | none of these |
| Answer» C. change is potential is minimum. | |
| 2541. |
The potential at the point x (measured in\[\mu m\]) due to some charges situated on the x-axis is given by \[V(x)=20({{x}^{2}}-4)\] volt. The electric field E at \[x=4\mu m\] |
| A. | \[\left( 10/9 \right)\text{ }volt/\mu m\]and in the +ve x direction |
| B. | \[\left( 5/3 \right)\text{ }volt/\mu m\]and in the -ve x direction |
| C. | \[\left( 5/3 \right)\text{ }volt/\mu m\] and in the +ve x direction |
| D. | \[\left( 10/9 \right)\text{ }volt/\mu m\]and in the -ve x direction |
| Answer» B. \[\left( 5/3 \right)\text{ }volt/\mu m\]and in the -ve x direction | |
| 2542. |
There is an infinite straight chain of alternating charges q and -q. The distance between the two neighboring charges is equal to a. Find the interaction energy of any charge with all the other charges. |
| A. | \[-\frac{2{{q}^{2}}}{4\pi {{\varepsilon }_{0}}a}\] |
| B. | \[\frac{2{{q}^{2}}{{\log }_{e}}2}{4\pi {{\varepsilon }_{0}}a}\] |
| C. | \[-\frac{2{{q}^{2}}{{\log }_{e}}2}{4\pi {{\varepsilon }_{0}}a}\] |
| D. | Zero |
| Answer» D. Zero | |
| 2543. |
Four points a, b, c and d are set at equal distance The electrostatic potential \[{{V}_{a}},{{V}_{b}},{{V}_{c}}\text{ and }{{V}_{d}}\]would satisfy the following relation: |
| A. | \[{{V}_{a}}>{{V}_{b}}>{{V}_{c}}>{{V}_{d}}\] |
| B. | \[{{V}_{a}}>{{V}_{b}}={{V}_{d}}>{{V}_{c}}\] |
| C. | \[{{V}_{a}}>{{V}_{c}}={{V}_{b}}={{V}_{d}}\] |
| D. | \[{{V}_{b}}={{V}_{d}}>{{V}_{a}}>{{V}_{c}}\] |
| Answer» C. \[{{V}_{a}}>{{V}_{c}}={{V}_{b}}={{V}_{d}}\] | |
| 2544. |
A conducting sphere of radius R is given a charge Q. The electric potential and the electric field at the center of the sphere respectively are: |
| A. | \[0\text{ and }\frac{Q}{4\pi \varepsilon {{ }_{0}}{{R}^{2}}}\] |
| B. | \[\frac{Q}{4\pi \varepsilon {{ }_{0}}R}\text{ and 0}\] |
| C. | \[\frac{Q}{4\pi \varepsilon {{ }_{0}}R}\text{ and }\frac{Q}{4\pi \varepsilon {{ }_{0}}{{R}^{2}}}\text{ }\] |
| D. | Both are 0 |
| Answer» C. \[\frac{Q}{4\pi \varepsilon {{ }_{0}}R}\text{ and }\frac{Q}{4\pi \varepsilon {{ }_{0}}{{R}^{2}}}\text{ }\] | |
| 2545. |
A plastic disc is charged on one side with a uniform surface charge density \[\sigma \]and then three quadrant of the disk are removed. The remaining quadrant is shown in figure, with V=0 at infinity, the potential due to the remaining quadrant point P is |
| A. | \[\frac{\sigma }{2{{\in }_{0}}}\left[ {{\left( {{r}^{2}}+{{R}^{2}} \right)}^{1/2}}-r \right]\] |
| B. | \[\frac{\sigma }{2{{\in }_{0}}}\left[ R-r \right]\] |
| C. | \[\frac{\sigma }{8{{\in }_{0}}}\left[ {{\left( {{r}^{2}}+{{R}^{2}} \right)}^{1/2}}-r \right]\] |
| D. | none of these |
| Answer» D. none of these | |
| 2546. |
A point charge of magnitude \[+1\mu C\] is fixed at (0, 0). An isolated uncharged spherical conductor, is fixed with its center at (4, 0, 0). The potential and the induced electric field at the center of the sphere is: |
| A. | \[1.8\times {{10}^{5}}V\text{ and }-5.625\times {{10}^{6}}V/m\] |
| B. | 0 V and 0 V/m |
| C. | \[2.25\times {{10}^{5}}V\text{ and }-5.625\times {{10}^{6}}V/m\] |
| D. | \[2.25\times {{10}^{5}}V\text{ and 0 V/m}\] |
| Answer» D. \[2.25\times {{10}^{5}}V\text{ and 0 V/m}\] | |
| 2547. |
Two concepts spheres of radii R and r have similar charges with equal surface charge densities \[\left( \sigma \right).\] what is the electric potential at their common center? |
| A. | \[\sigma /{{\varepsilon }_{0}}\] |
| B. | \[\frac{\sigma }{{{\varepsilon }_{0}}}\left( R-r \right)\] |
| C. | \[\frac{\sigma }{{{\varepsilon }_{0}}}\left( R+r \right)\] |
| D. | None of these |
| Answer» D. None of these | |
| 2548. |
From a point charge, there is a fixed point A. At A, there is an electric field of 500 V/m and potential difference of 3000 V. Distance between point charge and A will be? |
| A. | 6 m |
| B. | 12 m |
| C. | 16 m |
| D. | 24 m |
| Answer» B. 12 m | |
| 2549. |
Four identical particles each of mass m and charge q are kept at the four comers of a square of length L. The final velocity of these particles after setting them free will be |
| A. | \[{{\left[ \frac{K{{q}^{2}}}{mL}\left( 5.4 \right) \right]}^{1/2}}\] |
| B. | \[{{\left[ \frac{K{{q}^{2}}}{mL}\left( 1.35 \right) \right]}^{1/2}}\] |
| C. | \[{{\left[ \frac{K{{q}^{2}}}{mL}\left( 2.7 \right) \right]}^{1/2}}\] |
| D. | None of these |
| Answer» D. None of these | |
| 2550. |
A, B and C are three points in a uniform electric field. The electric potential is |
| A. | maximum B |
| B. | maximum C |
| C. | same at all the three points A, B and C |
| D. | maximum A |
| Answer» B. maximum C | |