MCQOPTIONS
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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.
| 2701. |
A system consists of a uniform charged sphere of radius R and a surrounding medium filled by a charge with the volume density \[\rho =\frac{\alpha }{r},\] where \[\alpha \]a positive constant is and r is the distance from the center of the charge. The charge of the sphere for which the electric field intensity E outside the sphere is independent of r is- |
| A. | \[\pi {{R}^{2}}\alpha \] |
| B. | \[4\pi {{R}^{2}}\alpha \] |
| C. | \[2\pi {{R}^{2}}\alpha \] |
| D. | \[3\pi {{R}^{2}}\alpha /4\] |
| Answer» D. \[3\pi {{R}^{2}}\alpha /4\] | |
| 2702. |
A disc of radius a/4 having a uniformly distributed charge 6C is placed in the x-y plane with its center at (-a/2, 0, 0). A rod of length a carrying a uniformly distributed charge 8C is placed on the x-axis from \[x=a/4\] to \[x=5a/4\]. Two point charges -7C and 3C are placed at (a/4, -a/4, 0) and (-3a/4, 3a/4, 0), respectively. Consider a cubical surface formed by six surfaces \[x=\pm a/2,y=\pm a/2,z=\pm a/2.\] The electric flux through this cubical surface is |
| A. | \[\frac{-2C}{{{\varepsilon }_{0}}}\] |
| B. | \[\frac{2C}{{{\varepsilon }_{0}}}\] |
| C. | \[\frac{10C}{{{\varepsilon }_{0}}}\] |
| D. | \[\frac{12C}{{{\varepsilon }_{0}}}\] |
| Answer» B. \[\frac{2C}{{{\varepsilon }_{0}}}\] | |
| 2703. |
The inward and outward electric flux for a closed surface in units of \[N-{{m}^{2}}/C\]are respectively \[8\times {{10}^{3}}\] and \[4\times {{10}^{3}}.\] Then the total charge inside the surface is [where \[{{\varepsilon }_{0}}\]= permittivity constant] |
| A. | \[4\times {{10}^{3}}C\] |
| B. | \[3.14\,\,N{{m}^{2}}/C\] |
| C. | \[\frac{(-\,4\times {{10}^{3}})}{\varepsilon }C\] |
| D. | \[-\,4\times {{10}^{3}}{{\varepsilon }_{0}}C\] |
| Answer» E. | |
| 2704. |
Consider an electric field \[\vec{E}={{E}_{0}}\hat{x}\] where \[{{E}_{0}}\] is a constant. The flux through the shaded area (as shown in the figure) due to this field is |
| A. | \[2{{E}_{0}}{{a}^{2}}\] |
| B. | \[\sqrt{2}{{E}_{0}}{{a}^{2}}\] |
| C. | \[{{E}_{0}}{{a}^{2}}\] |
| D. | \[\frac{{{E}_{0}}{{a}^{2}}}{\sqrt{2}}\] |
| Answer» D. \[\frac{{{E}_{0}}{{a}^{2}}}{\sqrt{2}}\] | |
| 2705. |
A loop of diameter d is rotated in a uniform electric field until the position of maximum electric flux is found. The flux in this position is measured to be \[\phi .\] What is the electric field strength? |
| A. | \[\frac{4\phi }{\pi {{d}^{2}}}\] |
| B. | \[\frac{2\phi }{\pi {{d}^{2}}}\] |
| C. | \[\frac{\phi }{\pi {{d}^{2}}}\] |
| D. | \[\frac{\pi \phi {{d}^{2}}}{4}\] |
| Answer» B. \[\frac{2\phi }{\pi {{d}^{2}}}\] | |
| 2706. |
A solid conducting sphere of radius a has a net positive charge 2Q. A concluding spherical shell of inner radius b and outer radius c is concentric with the solid sphere and has a net charge-Q. The surface charge density on the inner and outer surfaces charge density on the inner and outer surfaces of the spherical shell will be |
| A. | \[-\frac{2Q}{4\pi {{b}^{2}}},\frac{Q}{4\pi {{c}^{2}}}\] |
| B. | \[-\frac{Q}{4\pi {{b}^{2}}},\frac{Q}{4\pi {{c}^{2}}}\] |
| C. | \[0,\frac{Q}{4\pi {{c}^{2}}}\] |
| D. | None of the above |
| Answer» B. \[-\frac{Q}{4\pi {{b}^{2}}},\frac{Q}{4\pi {{c}^{2}}}\] | |
| 2707. |
If the electric flux entering and leaving an enclosed surface respectively is \[{{\phi }_{1}}\]and\[{{\phi }_{2}}\], the electric charge inside the surface will be |
| A. | \[\left( {{\phi }_{2}}+{{\phi }_{2}} \right)\times {{\varepsilon }_{0}}\] |
| B. | \[\left( {{\phi }_{2}}-{{\phi }_{2}} \right)\times {{\varepsilon }_{0}}\] |
| C. | \[\left( {{\phi }_{1}}+{{\phi }_{2}} \right)\times {{\varepsilon }_{0}}\] |
| D. | \[\left( {{\phi }_{1}}-{{\phi }_{2}} \right)\times {{\varepsilon }_{0}}\] |
| Answer» E. | |
| 2708. |
Electric flux over a surface in an electric field may |
| A. | positive |
| B. | negative |
| C. | zero |
| D. | All of these |
| Answer» E. | |
| 2709. |
A point charge +Q is positioned at the center of the base of a square pyramid as shown. The flux through one of the four identical upper faces of the pyramid is |
| A. | \[\frac{Q}{16{{\varepsilon }_{0}}}\] |
| B. | \[\frac{Q}{4{{\varepsilon }_{0}}}\] |
| C. | \[\,\frac{Q}{8{{\varepsilon }_{0}}}\] |
| D. | \[0\] |
| Answer» D. \[0\] | |
| 2710. |
Two point dipoles \[p\hat{k}\] and \[\frac{P}{2}\hat{k}\] are located at (0, 0, 0) and (1m, 0, 2m) respectively. The resultant electric field due to the two dipoles at the point (1m, 0, 0) is |
| A. | \[\frac{9P}{32\pi {{\in }_{0}}}\hat{k}\] |
| B. | \[\frac{-7P}{32\pi {{\in }_{0}}}\hat{k}\] |
| C. | \[\frac{7P}{32\pi {{\in }_{0}}}\hat{k}\] |
| D. | \[\frac{6P}{{{\in }_{0}}}\hat{k}\] |
| Answer» C. \[\frac{7P}{32\pi {{\in }_{0}}}\hat{k}\] | |
| 2711. |
An electric dipole of moment \[\vec{P}\] is placed in a uniform electric field \[\vec{E}\]. If the dipole is slightly rotated about an axis perpendicular to the plane containing \[\vec{E}\] and \[\vec{P}\] passing through the center of the dipole, the dipole executes simple harmonic motion. Consider I to be the moment of inertia of the dipole about the axis of rotation. What is the time period of such oscillation? |
| A. | \[\sqrt{\left( pE/I \right)}\] |
| B. | \[2\pi \sqrt{\left( I/pE \right)}\] |
| C. | \[2\pi \sqrt{\left( I/2pE \right)}\] |
| D. | None of these |
| Answer» C. \[2\pi \sqrt{\left( I/2pE \right)}\] | |
| 2712. |
A particle of charge - q and mass m moves in a circle of radius r around an infinitely long line charge of linear charge density \[+\lambda .\]Then time period will be |
| A. | \[T=2\pi r\sqrt{\frac{m}{2k\lambda q}}\] |
| B. | \[{{T}^{2}}=\frac{4{{\pi }^{2}}m}{2k\lambda q}{{r}^{3}}\] |
| C. | \[T=\frac{1}{2\pi r}\sqrt{\frac{2k\lambda q}{m}}\] |
| D. | \[T=\frac{1}{2\pi r}\sqrt{\frac{m}{2k\lambda q}}\] |
| Answer» B. \[{{T}^{2}}=\frac{4{{\pi }^{2}}m}{2k\lambda q}{{r}^{3}}\] | |
| 2713. |
Two positive ions, each carrying a charge q, are separated by a distance d. If F is the force of repulsion between the ions, the number of electrons missing from each ion will be (e being the charge of an electron) |
| A. | \[\frac{4\pi {{\varepsilon }_{0}}F{{d}^{2}}}{{{e}^{2}}}\] |
| B. | \[\sqrt{\frac{4\pi {{\varepsilon }_{0}}F{{e}^{2}}}{{{d}^{2}}}}\] |
| C. | \[\sqrt{\frac{4\pi {{\varepsilon }_{0}}F{{d}^{2}}}{{{e}^{2}}}}\] |
| D. | \[\frac{4\pi {{\varepsilon }_{0}}F{{d}^{2}}}{{{q}^{2}}}\] |
| Answer» D. \[\frac{4\pi {{\varepsilon }_{0}}F{{d}^{2}}}{{{q}^{2}}}\] | |
| 2714. |
Consider a uniform spherical charge distribution of radius \[{{R}_{1}}\] centered at the origin O. In this distribution, a spherical cavity of radius \[{{R}_{2}}\], centered at P with distance \[OP=a={{R}_{1}}-{{R}_{2}}\](see figure) is made. If the electric field inside the cavity at position \[\vec{r}\]is \[\vec{E}\overrightarrow{(r)}\], then the correct statement is |
| A. | \[\vec{E}\] is uniform, its magnitude is independent of \[{{R}_{2}}\]but its direction depends on \[\vec{r}\] |
| B. | \[\vec{E}\] is uniform, its magnitude depends on \[{{R}_{2}}\]and its direction depends on \[\vec{r}\] |
| C. | \[\vec{E}\] is uniform, its magnitude depends of a but its direction depends on \[\vec{a}\] |
| D. | \[\vec{E}\] is uniform and both its magnitude and direction depends on \[\vec{a}\] |
| Answer» E. | |
| 2715. |
The electric field intensity at the center of a uniformly charged hemispherical shell is \[{{E}_{0}}.\]Now two portions of the remaining portion is shown in Fig. If \[\alpha =\beta =\pi /3\], then the electric field intensity at the center due to the remaining portion is |
| A. | \[{{E}_{0}}/3\] |
| B. | \[{{E}_{0}}/6\] |
| C. | \[{{E}_{0}}/2\] |
| D. | Information incomplete |
| Answer» D. Information incomplete | |
| 2716. |
A thin conducting ring of radius R is given a charge +Q. The electric field at the center O of the ring due to the charge on the part AKB of the ring is E. The electric field at the center due to the charge on the part ACDB of the ring is |
| A. | E along KO |
| B. | E along OK |
| C. | E along KO |
| D. | 3E along OK |
| Answer» C. E along KO | |
| 2717. |
The thickness of a flat sheet of metal foil is d, and its area is S.A charge q is located at a distance \[\ell \]from the centre of the sheet such that \[d |
| A. | \[\frac{{{q}^{2}}Sd}{8{{\pi }^{2}}{{\varepsilon }_{0}}{{\ell }^{5}}}\] |
| B. | \[\frac{{{q}^{2}}Sd}{4{{\pi }^{2}}{{\varepsilon }_{0}}{{\ell }^{5}}}\] |
| C. | \[\frac{{{q}^{2}}Sd}{6{{\pi }^{2}}{{\varepsilon }_{0}}{{\ell }^{5}}}\] |
| D. | \[\frac{2{{q}^{2}}Sd}{3{{\pi }^{2}}{{\varepsilon }_{0}}{{\ell }^{5}}}\] |
| Answer» B. \[\frac{{{q}^{2}}Sd}{4{{\pi }^{2}}{{\varepsilon }_{0}}{{\ell }^{5}}}\] | |
| 2718. |
A charge is situated at a certain distance from an electric dipole in the end-on position experiences a force F. If the distance of the charge is doubled, the force acting on the charge will be |
| A. | F/4 |
| B. | F/8 |
| C. | 2F |
| D. | F/2 |
| Answer» C. 2F | |
| 2719. |
A point charge \[50\mu C\] is located in the x-y plane at a point whose position vector is \[\vec{r}=\left( 2\hat{i}+3\hat{j} \right)m.\]Then electric field at the point whose position vector is \[\vec{r}=\left( 8\hat{i}-5\hat{j} \right)m.\](in vector form) will be |
| A. | \[90\left( -3\hat{i}+4\hat{j} \right)V/m\]\[\] |
| B. | \[900\left( 3\hat{i}-4\hat{j} \right)V/m\] |
| C. | \[90\left( 3\hat{i}-4\hat{j} \right)V/m\] |
| D. | (d)\[900\left( -3\hat{i}+4\hat{j} \right)V/m\] |
| Answer» C. \[90\left( 3\hat{i}-4\hat{j} \right)V/m\] | |
| 2720. |
A ring of charge with radius 0.5 m has \[0.002\pi m\]gap. If the ring carries a charge of +1 C, the electric field at the center is |
| A. | \[7.5\times {{10}^{7}}N{{C}^{-1}}\] |
| B. | \[7.2\times {{10}^{7}}N{{C}^{-1}}\] |
| C. | \[6.2\times {{10}^{7}}N{{C}^{-1}}\] |
| D. | \[6.5\times {{10}^{7}}N{{C}^{-1}}\] |
| Answer» C. \[6.2\times {{10}^{7}}N{{C}^{-1}}\] | |
| 2721. |
A particle of charge q and mass m moves rectilinearly under the action of electric field \[E=A-Bx,\]where A and B are positive constants and x is distance from the point where particle was initially at rest then the distance traveled by the particle before coming to rest and acceleration of particle at that moment are respectively: |
| A. | \[\frac{2A}{B},0\] |
| B. | \[0,-\frac{qA}{m}\] |
| C. | \[\frac{2A}{B},-\frac{qA}{m}\] |
| D. | \[\frac{-2A}{B},-\frac{qA}{m}\] |
| Answer» D. \[\frac{-2A}{B},-\frac{qA}{m}\] | |
| 2722. |
Two very long line charges of uniform charge density \[+\lambda \]and \[-\lambda \]are placed along same line with the separation between the nearest ends being 2a, as shown in figure. The electric field intensity at point O is |
| A. | \[\frac{\lambda }{2\pi {{\varepsilon }_{0}}a}\] |
| B. | 0 |
| C. | \[\frac{\lambda }{\pi {{\varepsilon }_{0}}a}\] |
| D. | \[\frac{\lambda }{4\pi {{\varepsilon }_{0}}a}\] |
| Answer» B. 0 | |
| 2723. |
A spherical portion has been removed from a solid sphere having a charge distributed uniformly in its volume as shown in the figure. The electric field inside the emptied space is |
| A. | zero everywhere |
| B. | non-zero and uniform |
| C. | non-uniform |
| D. | zero only at its center |
| Answer» C. non-uniform | |
| 2724. |
Figure shows an electric quadrupole, with quadruple moment \[(Q\text{ }=\text{ }2q{{\ell }^{2}}).\]The electric field at a distance from its center at the axis of the quadrupole is given by |
| A. | \[\left( \frac{1}{4\pi {{\in }_{0}}} \right)\frac{Q}{{{r}^{4}}}\] |
| B. | \[\left( \frac{1}{4\pi {{\in }_{0}}} \right)\frac{2Q}{{{r}^{4}}}\] |
| C. | \[\left( \frac{1}{4\pi {{\in }_{0}}} \right)\frac{3Q}{{{r}^{4}}}\] |
| D. | None of these |
| Answer» D. None of these | |
| 2725. |
Point charge q moves from point P to point S along the path PQRS (as shown in fig.) in a uniform electric field E pointing co-parallel to the positive direction of X-axis. The coordinates of the points P, Q, R and S are (a, b, 0), (2a, 0, 0), (a, -b, 0) and (0, 0, 0) respectively. The work done by the field in the above case is given by the expression |
| A. | \[qEA\] |
| B. | \[-qEA\] |
| C. | \[qEA\sqrt{2}\] |
| D. | \[qE\sqrt{\left[ {{\left( 2a \right)}^{2}}+{{b}^{2}} \right]}\] |
| Answer» C. \[qEA\sqrt{2}\] | |
| 2726. |
An electric dipole, consisting of two opposite charges of \[2\times {{10}^{-\,6}}C\] each separated by a distance 3 cm is placed in an electric field of \[2\times {{10}^{5}}N/C.\] Torque acting on the dipole is |
| A. | \[12\times {{10}^{-1}}N-m\] |
| B. | \[12\times {{10}^{-2}}N-m\] |
| C. | \[12\times {{10}^{-3}}N-m\] |
| D. | \[12\times {{10}^{-4}}N-m\] |
| Answer» D. \[12\times {{10}^{-4}}N-m\] | |
| 2727. |
Two identical electric dipoles are arranged on x-axis as shown in figure. Electric field at the origin will be |
| A. | Zero |
| B. | \[\frac{kp\sqrt{2}}{{{r}^{3}}}\hat{j}\] |
| C. | \[\frac{-kp\sqrt{2}}{{{r}^{3}}}\hat{j}\] |
| D. | \[\frac{-kp}{{{r}^{3}}}\hat{i}-\frac{-kp}{{{r}^{3}}}\hat{j}\] |
| Answer» D. \[\frac{-kp}{{{r}^{3}}}\hat{i}-\frac{-kp}{{{r}^{3}}}\hat{j}\] | |
| 2728. |
A liquid drop having 6 excess electrons is kept stationary under a uniform electric field of\[25.5KV{{m}^{-1}}\]. The radius of the drop is (neglect buotany) |
| A. | \[4.3\times {{10}^{-7}}m\] |
| B. | \[7.3\times {{10}^{-7}}m\] |
| C. | \[0.078\times {{10}^{-7}}m\] |
| D. | \[3.4\times {{10}^{-7}}m\] |
| Answer» C. \[0.078\times {{10}^{-7}}m\] | |
| 2729. |
Two insulated charged metallic sphere P and Q have their centers separated by distance of 60 cm. The radii of P and Q are negligible |
| A. | \[5.2\times {{10}^{-4}}N\] |
| B. | c \[2.5\times {{10}^{-3}}N\] |
| C. | \[1.5\times {{10}^{-3}}N\] |
| D. | \[3.5\times {{10}^{-4}}N\] |
| Answer» C. \[1.5\times {{10}^{-3}}N\] | |
| 2730. |
In the figure the electric lines on the right have twice the separation of those on the left. If a charge particle takes time t to move a distance x in left region, then it will take time to travel the same distance in the right side region is: |
| A. | \[\frac{t}{2}\] |
| B. | \[t\] |
| C. | \[\sqrt{2}t\] |
| D. | \[2t\] |
| Answer» D. \[2t\] | |
| 2731. |
Let \[\rho \left( r \right)=\frac{Q}{\pi {{R}^{4}}}r\] be the charge density distribution for a solid sphere of radius R and total charge Q. For a point ?P? inside the sphere at distance \[{{r}_{1}}\] from the center of the sphere, the magnitude of electric field is: |
| A. | \[\frac{Q}{4\pi {{\in }_{0}}{{R}_{1}}^{2}}\]\[\] |
| B. | \[\frac{Qr_{1}^{2}}{4\pi {{\in }_{0}}{{R}^{4}}}\] |
| C. | \[\frac{Qr_{1}^{2}}{3\pi {{\in }_{0}}{{R}^{4}}}\] |
| D. | \[0\] |
| Answer» C. \[\frac{Qr_{1}^{2}}{3\pi {{\in }_{0}}{{R}^{4}}}\] | |
| 2732. |
On decreasing the distance between the two charges of a dipole which is perpendicular to electric field and decreasing the angle between the dipole and electric field, the torque on the dipole |
| A. | increases |
| B. | decreases |
| C. | remains same |
| D. | cannot be predicated |
| Answer» C. remains same | |
| 2733. |
If the dipole of moment \[2.57\times {{10}^{-17}}cm\] is placed into an electric field of magnitude \[3.0\times {{10}^{4}}N/C\]such that the fields lines are aligned at \[30{}^\circ \] with the line joining P to the dipole, what torque acts on the dipole? |
| A. | \[7.7\times {{10}^{-13}}Nm\] |
| B. | \[3.855\times {{10}^{-13}}Nm\] |
| C. | \[3.855\times {{10}^{-15}}Nm\] |
| D. | \[7.7\times {{10}^{-15}}Nm\] |
| Answer» C. \[3.855\times {{10}^{-15}}Nm\] | |
| 2734. |
Intensity of an electric field (E) depends on distance r, due to a dipole, is related as |
| A. | \[E\propto \frac{1}{r}\] |
| B. | \[E\propto \frac{1}{{{r}^{2}}}\] |
| C. | \[E\propto \frac{1}{{{r}^{3}}}\] |
| D. | \[E\propto \frac{1}{{{r}^{4}}}\] |
| Answer» D. \[E\propto \frac{1}{{{r}^{4}}}\] | |
| 2735. |
ABC is an equilateral triangle. Charges +q are placed at each corner as shown in fig. The electric intensity at center O will be |
| A. | \[\frac{1}{4\pi {{\in }_{0}}}\frac{q}{r}\] |
| B. | \[\frac{1}{4\pi {{\in }_{0}}}\frac{q}{{{r}^{2}}}\] |
| C. | \[\frac{1}{4\pi {{\in }_{0}}}\frac{3q}{{{r}^{2}}}\] |
| D. | Zero |
| Answer» E. | |
| 2736. |
Two charge q and -3q are placed fixed on x-axis separated by distance d. Where should experience any force? |
| A. | \[\frac{d-\sqrt{2}d}{2}\] |
| B. | \[\frac{d+\sqrt{3}d}{2}\] |
| C. | \[\frac{d+3d}{2}\] |
| D. | \[\frac{d-\sqrt{5}d}{2}\] |
| Answer» C. \[\frac{d+3d}{2}\] | |
| 2737. |
The number of electric lines of force that radiate outwards from one coulomb of charge in vacuum is |
| A. | \[1.13\times {{10}^{11}}\] |
| B. | \[1.13\times {{10}^{10}}\] |
| C. | \[0.61\times {{10}^{11}}\] |
| D. | \[0.61\times {{10}^{9}}\] |
| Answer» B. \[1.13\times {{10}^{10}}\] | |
| 2738. |
A hollow insulated conduction sphere is given a positive charge of \[10\mu C.\] What will be the electric field at the center of the sphere if its radius is 2m? |
| A. | Zero |
| B. | \[5\mu C{{m}^{-2}}\] |
| C. | \[20\mu C{{m}^{-2}}\] |
| D. | \[8\mu C{{m}^{-2}}\] |
| Answer» B. \[5\mu C{{m}^{-2}}\] | |
| 2739. |
The insulation property of air breaks down when the electric field is \[3\times {{10}^{6}}V{{m}^{-1}}.\] The maximum charge that can be given to a sphere of diameter 5 m is approximately |
| A. | \[2\times {{10}^{-2}}C\] |
| B. | \[2\times {{10}^{-3}}C\] |
| C. | \[2\times {{10}^{-4}}C\] |
| D. | \[2\times {{10}^{-5}}C\] |
| Answer» C. \[2\times {{10}^{-4}}C\] | |
| 2740. |
The electric field intensity just sufficient to balance the earth?s gravitational attraction on an electron will be: (given mass and charge of an electron respectively are \[9.1\times {{10}^{-31}}kg\]and \[1.6\times {{10}^{-19}}C.\]) |
| A. | \[-\,5.6\times {{10}^{-11}}N/C\] |
| B. | \[-\,4.8\times {{10}^{-15}}N/C\] |
| C. | \[-\,1.6\times {{10}^{-19}}N/C\] |
| D. | \[-\,3.2\times {{10}^{-19}}N/C\] |
| Answer» B. \[-\,4.8\times {{10}^{-15}}N/C\] | |
| 2741. |
If electric field in a region is radially outward with magnitude \[E=Ar\], the charge contained in a sphere of radius r centered at the origin is |
| A. | \[\frac{1}{4\pi {{\varepsilon }_{0}}}A{{r}^{3}}\] |
| B. | \[A{{r}^{3}}4\pi {{\varepsilon }_{0}}\] |
| C. | \[\frac{1}{4\pi {{\varepsilon }_{0}}}\frac{A}{{{r}^{3}}}\] |
| D. | \[\frac{4\pi {{\varepsilon }_{0}}A}{{{r}^{3}}}\] |
| Answer» C. \[\frac{1}{4\pi {{\varepsilon }_{0}}}\frac{A}{{{r}^{3}}}\] | |
| 2742. |
A rod of length 2.4 m and radius 4.6 mm carries a negative charge of \[4.2\times {{10}^{-7}}C\] spread uniformly over it surface. The electric field near the mid-point of the rod, at a point on its surface is |
| A. | \[-\,8.6\times {{10}^{5}}N{{C}^{-1}}\] |
| B. | \[8.6\times {{10}^{4}}N{{C}^{-1}}\] |
| C. | \[-\,6.7\times {{10}^{5}}N{{C}^{-1}}\] |
| D. | \[6.7\times {{10}^{4}}N{{C}^{-1}}\] |
| Answer» D. \[6.7\times {{10}^{4}}N{{C}^{-1}}\] | |
| 2743. |
When an electric dipole \[\vec{P}\] is placed in a uniform electric field E then at what angle between P and \[\vec{E}\] the value of torque will be maximum? |
| A. | \[90{}^\circ \] |
| B. | \[0{}^\circ \] |
| C. | \[180{}^\circ \] |
| D. | \[45{}^\circ \] |
| Answer» B. \[0{}^\circ \] | |
| 2744. |
Two identical beads each have a mass m and charge q. When placed in a hemispherical bowl of radius R with frictionless, nonconductive walls, the beads move, and at equilibrium the distance between them is R (Fig.). Determine the charge on each bead. |
| A. | \[R{{\left( \frac{mg}{{{k}_{e}}\sqrt{3}} \right)}^{1/2}}\] |
| B. | \[R{{\left( \frac{mg}{{{k}_{e}}\sqrt{2}} \right)}^{1/2}}\] |
| C. | \[R{{\left( \frac{mg}{{{k}_{e}}2\sqrt{3}} \right)}^{1/2}}\] |
| D. | \[R{{\left( \frac{2\,mg}{{{k}_{e}}\sqrt{3}} \right)}^{1/2}}\] |
| Answer» B. \[R{{\left( \frac{mg}{{{k}_{e}}\sqrt{2}} \right)}^{1/2}}\] | |
| 2745. |
The force between two small charged spheres having charges of \[1\times {{10}^{-7}}C\] and \[2\times {{10}^{-7}}C\] |
| A. | \[4.5\times {{10}^{-}}^{2}N\] |
| B. | \[4.5\times {{10}^{-}}^{3}N\] |
| C. | \[5.4\times {{10}^{-2}}N\] |
| D. | \[5.4\times {{10}^{-3}}N\] |
| Answer» C. \[5.4\times {{10}^{-2}}N\] | |
| 2746. |
Two small balls having the same mass and charge and located on the same vertical at heights \[{{h}_{1}}\] and \[{{h}_{2}}\] are thrown in the same direction along the horizontal at the same velocity v. The first ball touches the ground at a distance \[\ell \] from the initial vertical. At what height \[{{H}_{2}}\]will the second ball be at this instant? The air drag and the effect of the charges induced on the ground should be neglected. |
| A. | \[{{h}_{1}}+{{h}_{2}}-g{{\left( \frac{\ell }{v} \right)}^{2}}\] |
| B. | \[{{h}_{1}}-{{h}_{2}}-g{{\left( \frac{\ell }{v} \right)}^{2}}\] |
| C. | \[{{h}_{1}}+{{h}_{2}}-g{{\left( \frac{\ell }{v} \right)}^{1/2}}\] |
| D. | \[\frac{{{h}_{1}}+{{h}_{2}}}{2}-g{{\left( \frac{\ell }{v} \right)}^{2}}\] |
| Answer» B. \[{{h}_{1}}-{{h}_{2}}-g{{\left( \frac{\ell }{v} \right)}^{2}}\] | |
| 2747. |
Two identical blocks are kept on a frictionless horizontal table connected by a spring of stiffness k and of original length \[{{l}_{0}}.\] A total charge Q is distributed of spring at equilibrium of equal to x. Value of Q is |
| A. | \[2{{\ell }_{0}}\sqrt{4\pi {{\varepsilon }_{0}}k\left( {{\ell }_{0}}+x \right)}\] |
| B. | \[2x\sqrt{4\pi {{\varepsilon }_{0}}k\left( {{\ell }_{0}}+x \right)}\] |
| C. | \[2\left( {{\ell }_{0}}+x \right)\sqrt{4\pi {{\varepsilon }_{0}}kx}\] |
| D. | \[\left( {{\ell }_{0}}+x \right)\sqrt{4\pi {{\varepsilon }_{0}}kx}\] |
| Answer» D. \[\left( {{\ell }_{0}}+x \right)\sqrt{4\pi {{\varepsilon }_{0}}kx}\] | |
| 2748. |
Two particle of equal mass m and charge q are placed at a distance of 16 cm. They do not experience any force. The value of \[\frac{q}{m}\] is |
| A. | 1 |
| B. | \[\sqrt{\frac{\pi {{\varepsilon }_{0}}}{G}}\] |
| C. | \[\sqrt{\frac{G}{4\pi {{\varepsilon }_{0}}}}\] |
| D. | \[\sqrt{4\pi {{\varepsilon }_{0}}}\] |
| Answer» E. | |
| 2749. |
Three identical spheres, each having a charge q And radius R, are kept in such a way that each touches the other two. The magnitude of the electric force any sphere due to the other two is |
| A. | \[\frac{1}{4\pi {{\varepsilon }_{0}}}{{\left( \frac{q}{R} \right)}^{2}}\] |
| B. | \[\frac{\sqrt{3}}{4\pi {{\varepsilon }_{0}}}{{\left( \frac{q}{R} \right)}^{2}}\] |
| C. | \[\frac{\sqrt{3}}{16\pi {{\varepsilon }_{0}}}{{\left( \frac{q}{R} \right)}^{2}}\] |
| D. | \[\frac{\sqrt{5}}{16\pi {{\varepsilon }_{0}}}{{\left( \frac{q}{R} \right)}^{2}}\] |
| Answer» D. \[\frac{\sqrt{5}}{16\pi {{\varepsilon }_{0}}}{{\left( \frac{q}{R} \right)}^{2}}\] | |
| 2750. |
Force between two identical charges placed at a distance of r in vacuum is F, Now a slab of dielectric of dielectric contrant 4 is inserted between these two charges. If the thickness of the slab is r/2, then the force between the charges will become |
| A. | F |
| B. | \[\frac{3}{5}F\] |
| C. | \[\frac{4}{9}F\] |
| D. | \[\frac{F}{2}\] |
| Answer» D. \[\frac{F}{2}\] | |