Q. No.Three small identical bubbles of water having same charge on each coalesce to form a bigger bubble. Then the ratio of the potentials on one initial bubble and that on the resultant bigger bubble is:
1. \(1 : 3^{1/3}\)
2. \(1 : 2^{2/3}\)
3. \(3^{2/3} : 1\)
4. \(1 : 3^{2/3}\)
1. \(1 : 3^{1/3}\)
2. \(1 : 2^{2/3}\)
3. \(3^{2/3} : 1\)
4. \(1 : 3^{2/3}\)
Subtopic: Electric Potential |
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Five positive charges each having charge \(q\) are placed at the vertices of a pentagon as shown in the figure. The electric potential \((V)\) and the electric field \(\vec{(E)}\) at the centre \(O\) of the pentagon due to these five positive charges are:
1. \(V=\dfrac{5 q}{4 \pi \varepsilon_0 r} \text { and } \vec{E}=0\)
2. \(V=\dfrac{5 q}{4 \pi \varepsilon_0 r} \text { and } \vec{E}=\dfrac{5 \sqrt{3} q}{8 \pi \varepsilon_0 r^2} \hat{r}\)
3. \(V=\dfrac{5 q}{4 \pi \varepsilon_0 r} \text { and } \vec{E}=\dfrac{5 q}{4 \pi \varepsilon_0 r^2} \hat{r}\)
4. \(V=0 \text { and } \vec{E}=0\)
1. \(V=\dfrac{5 q}{4 \pi \varepsilon_0 r} \text { and } \vec{E}=0\)
2. \(V=\dfrac{5 q}{4 \pi \varepsilon_0 r} \text { and } \vec{E}=\dfrac{5 \sqrt{3} q}{8 \pi \varepsilon_0 r^2} \hat{r}\)
3. \(V=\dfrac{5 q}{4 \pi \varepsilon_0 r} \text { and } \vec{E}=\dfrac{5 q}{4 \pi \varepsilon_0 r^2} \hat{r}\)
4. \(V=0 \text { and } \vec{E}=0\)
Subtopic: Electric Potential |
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The electrostatic potential in a charged spherical region of radius \(r\) varies as \(V=a r^3+b,\) where \(a\) and \(b\) are constants. The total charge in the sphere of unit radius is \(\alpha \times \pi {a} \varepsilon_0.\) The value of \(\alpha\) is:
(permittivity of vacuum is \(\varepsilon_0\))
1. \(-12\)
2. \(-6\)
3. \(-9\)
4. \(-8\)
(permittivity of vacuum is \(\varepsilon_0\))
1. \(-12\)
2. \(-6\)
3. \(-9\)
4. \(-8\)
Subtopic: Electric Potential |
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There are three co-centric conducting spherical shells \(A,B~\text{and}~C\) of radii \(a,b~\text{and}~c\) respectively. The potential of the spheres \(A,B~\text{and}~C\) respectively, are:
1. \(\dfrac{1}{4 \pi \varepsilon_0}\left(\dfrac{q_1+q_2+q_3}{a}\right), \dfrac{1}{4 \pi \varepsilon_0}\left(\dfrac{q_1+q_2+q_3}{b}\right), \dfrac{1}{4 \pi \varepsilon_0}\left(\dfrac{q_1+q_2+q_3}{c}\right)\)
2. \( \dfrac{1}{4 \pi \varepsilon_0}\left(\dfrac{q_1+q_2+q_3}{a}\right), \dfrac{1}{4 \pi \varepsilon_0}\left(\dfrac{q_1+q_2}{b}+\dfrac{q_3}{c}\right), \dfrac{1}{4 \pi \varepsilon_0}\left(\dfrac{q_1}{a}+\dfrac{q_2}{b}+\dfrac{q_3}{c}\right) \)
3. \( \dfrac{1}{4 \pi \varepsilon_0}\left(\dfrac{q_1}{a}+\dfrac{q_2}{b}+\dfrac{q_3}{c}\right), \dfrac{1}{4 \pi \varepsilon_0}\left(\dfrac{q_1+q_2}{b}+\dfrac{q_3}{c}\right), \dfrac{1}{4 \pi \varepsilon_0}\left(\dfrac{q_1+q_2+q_3}{c}\right) \)
4. \(\dfrac{1}{4 \pi \varepsilon_0}\left(\dfrac{q_1}{a}+\dfrac{q_2}{b}+\dfrac{q_3}{c}\right), \dfrac{1}{4 \pi \varepsilon_0}\left(\dfrac{q_1+q_2+q_3}{b}\right), \dfrac{1}{4 \pi \varepsilon_0}\left(\dfrac{q_1+q_2+q_3}{c}\right)\)
1. \(\dfrac{1}{4 \pi \varepsilon_0}\left(\dfrac{q_1+q_2+q_3}{a}\right), \dfrac{1}{4 \pi \varepsilon_0}\left(\dfrac{q_1+q_2+q_3}{b}\right), \dfrac{1}{4 \pi \varepsilon_0}\left(\dfrac{q_1+q_2+q_3}{c}\right)\)
2. \( \dfrac{1}{4 \pi \varepsilon_0}\left(\dfrac{q_1+q_2+q_3}{a}\right), \dfrac{1}{4 \pi \varepsilon_0}\left(\dfrac{q_1+q_2}{b}+\dfrac{q_3}{c}\right), \dfrac{1}{4 \pi \varepsilon_0}\left(\dfrac{q_1}{a}+\dfrac{q_2}{b}+\dfrac{q_3}{c}\right) \)
3. \( \dfrac{1}{4 \pi \varepsilon_0}\left(\dfrac{q_1}{a}+\dfrac{q_2}{b}+\dfrac{q_3}{c}\right), \dfrac{1}{4 \pi \varepsilon_0}\left(\dfrac{q_1+q_2}{b}+\dfrac{q_3}{c}\right), \dfrac{1}{4 \pi \varepsilon_0}\left(\dfrac{q_1+q_2+q_3}{c}\right) \)
4. \(\dfrac{1}{4 \pi \varepsilon_0}\left(\dfrac{q_1}{a}+\dfrac{q_2}{b}+\dfrac{q_3}{c}\right), \dfrac{1}{4 \pi \varepsilon_0}\left(\dfrac{q_1+q_2+q_3}{b}\right), \dfrac{1}{4 \pi \varepsilon_0}\left(\dfrac{q_1+q_2+q_3}{c}\right)\)
Subtopic: Electric Potential |
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Two metal spheres of radius \(R \) and \(3R \) have same surface charge density \(σ.\) If they are brought in contact and then separated, the surface charge density on smaller and bigger sphere becomes \(σ_1 \) and \(σ_2\) respectively. The ratio \(\dfrac{σ_1}{σ_2} \) is:
1. \(\dfrac{1}{9}\)
2. \(9\)
3. \(\dfrac{1}{3}\)
4. \(3\)
1. \(\dfrac{1}{9}\)
2. \(9\)
3. \(\dfrac{1}{3}\)
4. \(3\)
Subtopic: Electric Potential |
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Given below are two statements:
In the light of the above statements, choose the most appropriate answer from the options given below:
| Assertion (A): | Work done in moving a test charge between two points inside a uniformly charged spherical shell is zero, no matter which path is chosen. |
| Reason (R): | Electrostatic potential inside a uniformly charged spherical shell is constant and is same as that on the surface of the shell. |
| 1. | Both (A) and (R) are True and (R) is the correct explanation of (A). |
| 2. | Both (A) and (R) are True but (R) is not the correct explanation of (A). |
| 3. | (A) is True but (R) is False. |
| 4. | (A) is False but (R) is True. |
Subtopic: Electric Potential |
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The electrostatic potential on the surface of uniformly charged spherical shell of radius \(R = 10 \text{ cm} \) is \(120 ~\text{V}.\) The potential at the centre of shell, at a distance \(r = 5 \text{ cm} \) from centre, and at a distance \(r = 15 \text{ cm} \) from the centre of the shell respectively, are:
| 1. | \(40~ \text{V}, 40~ \text{V}, 80~ \text{V}\) |
| 2. | \(0 ~\text{V}, 120~ \text{V}, 40~ \text{V}\) |
| 3. | \(0~\text{V}, 0~ \text{V}, 80 ~\text{V} \) |
| 4. | \(120 ~\text{V}, 120~ \text{V}, 80~ \text{V}\) |
Subtopic: Electric Potential |
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In the first configuration (1) as shown in the figure, four identical charges \(q_0\) are kept at the corners \(A, B, C \text { and } D~~\) of the square of side length \(a.\) In the second configuration (2), the same charges are shifted to mid points \(G, E, H\) and \(F\), of the square. If \(K=\dfrac{1}{4πε_0},\) the difference between the potential energies of configuration (2) and (1) is given by -
1.\(\dfrac{K q_0^2}{a}(3 \sqrt{2}-2) \)
2. \(\dfrac{K q_0^2}{a}(4-2 \sqrt{2})\)
3. \(\dfrac{K q_0^2}{a}(4 \sqrt{2}-2) \)
4. \(\dfrac{K q_0^2}{a}(3-\sqrt{2})\)
1.\(\dfrac{K q_0^2}{a}(3 \sqrt{2}-2) \)
2. \(\dfrac{K q_0^2}{a}(4-2 \sqrt{2})\)
3. \(\dfrac{K q_0^2}{a}(4 \sqrt{2}-2) \)
4. \(\dfrac{K q_0^2}{a}(3-\sqrt{2})\)
Subtopic: Electric Potential |
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Two charges \(7~\mu\text C\) and \(-4 \mu~\text C\) are placed at at \((-7~\text{cm},~0,~0)\) and \((7~\text{cm},~0,~0)\) respectively. Given, \(\epsilon_0 = 8.85×10^{-12}~\text {C}^2\text {N}^{-1} \text {m}^{-2}\) the electrostatic potential energy of charge configuration is:
1. \(-1.5~\text J\)
2. \(-1.2~\text J\)
3. \(-2.0~\text J\)
4. \(-1.8~\text J\)
1. \(-1.5~\text J\)
2. \(-1.2~\text J\)
3. \(-2.0~\text J\)
4. \(-1.8~\text J\)
Subtopic: Electric Potential |
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A short electric dipole with dipole moment \(p\) is placed at the origin \(O,\) orientated along the positive \(x\text-\)axis. Point A is located at distance \(r\) along the \(x\text-\)axis, and point \(B\) is located at distance \(2r\) along the \(y\text-\)axis. Given that the electric potential at \(A\) is \(V_0\) and the electric field at \(A\) is \(E_0,\) The electric potential and electric field at point \(B\) are:
| 1. | \(\dfrac{V_0}{2}\) and \(\dfrac{E_0}{16}\) | 2. | zero and \(\dfrac{E_0}{16}\) |
| 3. | zero and \(\dfrac{E_0}{8}\) | 4. | \(V_0\) and \(\dfrac{E_0}{4}\) |
Subtopic: Electric Potential |
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