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Q. No.Six charges \(+q,\) \(-q,\) \(+q,\) \(-q,\) \(+q\) and \(-q\) are fixed at the corners of a hexagon of side \(d\) as shown in the figure. The work done in bringing a charge \(q_0\) to the centre of the hexagon from infinity is: (\(\varepsilon_0\text-\)permittivity of free space)
| 1. | zero | 2. | \(\dfrac{-q^2}{4\pi\varepsilon_0d}\) |
| 3. | \(\dfrac{-q^2}{4\pi\varepsilon_0d}\Big(3-\dfrac{1}{\sqrt2}\Big)\) | 4. | \(\dfrac{-q^2}{4\pi\varepsilon_0d}\Big(6-\dfrac{1}{\sqrt2}\Big)\) |
Subtopic: Â Electric Potential Energy |
 85%
Level 1: 80%+
NEET - 2022
Hints
A positively charged particle \(+q\) is projected with speed \(v\) toward a fixed charge \(+Q,\) and rebounds after reaching a minimum distance \(r.\) What will be the new closest distance of approach if its initial velocity is doubled to \(2v\text{?}\)
| 1. | \(\dfrac{r}{4}\) | 2. | \(\dfrac{r}{2}\) |
| 3. | \(\dfrac{r}{16}\) | 4. | \(\dfrac{r}{8}\) |
Subtopic: Â Electric Potential Energy |
 72%
Level 2: 60%+
NEET - 2022
Hints
The value of the electric potential at a distance of \(9~\text{cm}\) from the point charge \(4\times10^{-7}~\text{C}\) is:
\(\left[\mathrm{Given}\dfrac{1}{4\pi\varepsilon_{0}}=9\times10^{9}~\text{N m}^{2}~\text{C}^{-2}\right]\)
\(\left[\mathrm{Given}\dfrac{1}{4\pi\varepsilon_{0}}=9\times10^{9}~\text{N m}^{2}~\text{C}^{-2}\right]\)
| 1. | \(4\times10^2~\text V\) | 2. | \(44.4~\text V\) |
| 3. | \(4.4\times10^5~\text V\) | 4. | \(4\times10^4~\text V\) |
Subtopic: Â Electric Potential |
 78%
Level 2: 60%+
NEET - 2024
Hints
Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).
In the light of the above statements, choose the correct answer from the options given below:
| Assertion (A): | The potential \((V)\) at any axial point, at \(2~\text m\) distance (\(r\)) from the centre of the dipole of dipole moment vector \(\vec P\) of magnitude, \(4\times10^{-6}~\text{C m},\) is \(\pm9\times10^3~\text{V}.\) (Take \({\dfrac{1}{4\pi\varepsilon_0}}=9\times10^9\) SI units) |
| Reason (R): | \(V=\pm{\dfrac{2P}{4\pi\varepsilon_0r^2}},\) where \(r\) is the distance of any axial point situated at \(2~\text m\) from the centre of the dipole. |
| 1. | Both (A) and (R) are True and (R) is not the correct explanation of (A). |
| 2. | (A) is True but (R) is False. |
| 3. | (A) is False but (R) is True. |
| 4. | Both (A) and (R) are True and (R) is the correct explanation of (A). |
Subtopic: Â Electric Potential |
 56%
Level 3: 35%-60%
NEET - 2024
Hints
A thin spherical shell is charged by some source. The potential difference between the two points \(C\) and \(P\) (in V) shown in the figure is:
( Take \(\dfrac{1}{4 \pi \epsilon_0}=9 \times 10^9\) SI units)
( Take \(\dfrac{1}{4 \pi \epsilon_0}=9 \times 10^9\) SI units)
| 1. | \(1 \times 10^5\) | 2. | \(0.5 \times 10^5\) |
| 3. | \(\text{zero}\) | 4. | \(3 \times 10^5\) |
Subtopic: Â Electric Potential |
 67%
Level 2: 60%+
NEET - 2024
Hints
If a conducting sphere of radius \(R\) is charged. Then the electric field at a distance \(r(r>R)\) from the centre of the sphere would be, (\(V=\) potential on the surface of the sphere):
| 1. | \(\dfrac{rV}{R^2}\) | 2. | \(\dfrac{R^2V}{r^3}\) |
| 3. | \(\dfrac{RV}{r^2}\) | 4. | \(\dfrac{V}{r}\) |
Subtopic: Â Electric Potential |
 50%
Level 3: 35%-60%
NEET - 2023
Hints
An electric dipole is placed as shown in the figure.
The electric potential (in \(10^2~\text{V}\)) at the point \(P\) due to the dipole is:
(\(\varepsilon_0=\) permittivity of free space and \(\dfrac{1}{4 \pi \varepsilon_0}=k\))
The electric potential (in \(10^2~\text{V}\)) at the point \(P\) due to the dipole is:
(\(\varepsilon_0=\) permittivity of free space and \(\dfrac{1}{4 \pi \varepsilon_0}=k\))
| 1. | \(\left(\dfrac{8}{3}\right)qk\) | 2. | \(\left(\dfrac{3}{8}\right)qk \) |
| 3. | \(\left(\dfrac{5}{8}\right)qk\) | 4. | \(\left(\dfrac{8}{5}\right)qk\) |
Subtopic: Â Energy of Dipole in an External Field |
 65%
Level 2: 60%+
NEET - 2023
Hints
A hollow metal sphere of radius \(R\) is given \(+Q\) charges to its outer surface. The electric potential at a distance \(\dfrac{R}{3}\) from the centre of the sphere will be:
| 1. | \(\dfrac{1}{4\pi \varepsilon_0}\dfrac{Q}{9R}\) | 2. | \(\dfrac{3}{4\pi \varepsilon_0}\dfrac{Q}{R}\) |
| 3. | \(\dfrac{1}{4\pi \varepsilon_0}\dfrac{Q}{3R}\) | 4. | \(\dfrac{1}{4\pi \varepsilon_0}\dfrac{Q}{R}\) |
Subtopic: Â Electric Potential |
 65%
Level 2: 60%+
NEET - 2022
Hints
Two hollow conducting spheres of radii \(R_1\) and \(R_2\) \(\left ( R_1\gg R_2 \right )\) are concentric and have equal charges. The potential would be:
| 1. | dependent on the material property of the sphere |
| 2. | more on the bigger sphere |
| 3. | more on the smaller sphere |
| 4. | equal on both the spheres |
Subtopic: Â Electric Potential |
 70%
Level 2: 60%+
PMT - 2022
Hints
Two charged spherical conductors of radii \(R_1\) and \(R_2\) are connected by a wire. The ratio of surface charge densities of spheres \(\left ( \dfrac{\sigma _{1}}{\sigma _{2}}\right ) \) is:
| 1. | \(\sqrt{\dfrac{R_1}{R_2}}\) | 2. | \(\dfrac{R^2_1}{R^2_2}\) |
| 3. | \(\dfrac{R_1}{R_2}\) | 4. | \(\dfrac{R_2}{R_1}\) |
Subtopic: Â Electric Potential |
 69%
Level 2: 60%+
NEET - 2021
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