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Q. No.A uniformly charged thin rod of length \(L\) carries a total charge \(q.\) The potential at a point \(A,\) on the perpendicular bisector of the rod, and at a distance \(L\) from its centre is:
\(\left(\text{take}~ k=\dfrac{1}{4\pi\varepsilon_0}\right) \)
1. \(\dfrac{kq}{L}\)
2. less than \(\dfrac{kq}{L}\)
3. greater than \(\dfrac{kq}{L}\)
4. zero
\(\left(\text{take}~ k=\dfrac{1}{4\pi\varepsilon_0}\right) \)
1. \(\dfrac{kq}{L}\)
2. less than \(\dfrac{kq}{L}\)
3. greater than \(\dfrac{kq}{L}\)
4. zero
Subtopic: Â Electric Potential |
Level 3: 35%-60%
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A charge is uniformly distributed on the circumference of a disc, and the potential at its centre is \(5\) volt. If the charge was uniformly distributed on the surface of this disc, the potential at a point \(P\) on its axis, at a distance equal to the disc's radius from its centre, equals:
1. \(10\) V
2. \(5 \sqrt 2\) V
3. \(10 \sqrt 2\) V
4. \(10 (\sqrt {2} -1)\) V
1. \(10\) V
2. \(5 \sqrt 2\) V
3. \(10 \sqrt 2\) V
4. \(10 (\sqrt {2} -1)\) V
Subtopic: Â Electric Potential |
Level 3: 35%-60%
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A semi-circular wire carries a positive charge \(Q\) distributed uniformly over its circumference, and lies with its center at the origin and its ends on the x-axis, as shown in the figure. A single point charge is to be placed so that the net electric field due to the charge \(Q\) and the new charge \((q_1)\) is zero at the origin. Let the distance of \(q_1\) from O be \(r_1\). The potential at the origin is also zero. Which of the following is correct?
\(1.~ r_{1}< \frac{r}{2} \\ 2.~ \frac{r}{2}<r_{1}< r \\ 3.~ r<r_{1}<\frac{3 r}{2}\\ 4.~ \frac{3 r}{2}<r_{1}\)
\(1.~ r_{1}< \frac{r}{2} \\ 2.~ \frac{r}{2}<r_{1}< r \\ 3.~ r<r_{1}<\frac{3 r}{2}\\ 4.~ \frac{3 r}{2}<r_{1}\)
Subtopic: Â Electric Potential |
Level 3: 35%-60%
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A sector of a circle (radius: \(R\)) carries a uniform surface charge \(Q\) distributed over it. The potential, due to this charge, at the centre of curvature if the sector \((O)\) is:
| 1. | \(\dfrac{kQ}{R}\) | 2. | \(\dfrac{kQ}{2R}\) |
| 3. | \(\dfrac{2kQ}{R}\) | 4. | \(\dfrac{kQ}{R}ln~2\) |
Subtopic: Â Electric Potential |
Level 3: 35%-60%
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An uncharged conducting sphere (radius: \(R\)) is placed in the field of a point charge \(Q.\) The potential of the point \(A\) on the sphere, nearest to \(Q,\) is: \(\bigg(k={\large\frac{1}{4\pi\varepsilon_0}}\bigg)\)
1. \(\Large\frac{kQ}{R}\)
2. \(\Large\frac{kQ}{d-R}\)
3. \(\Large\frac{kQ}{d-R^2/d}\)
4. \(\Large\frac{kQ}{d}\)
1. \(\Large\frac{kQ}{R}\)
2. \(\Large\frac{kQ}{d-R}\)
3. \(\Large\frac{kQ}{d-R^2/d}\)
4. \(\Large\frac{kQ}{d}\)
Subtopic: Â Electric Potential |
Level 3: 35%-60%
Hints
Three charges are placed at the three corners of an equilateral triangle as shown in the figure. The potential at the mid-point of a side with opposite charges is \(2~\text V.\) The potential at the centre of the triangle is:
| 1. | \(2~\text V\) | 2. | \(3~\text V\) |
| 3. | \(2\sqrt3~\text V\) | 4. | \(\dfrac{2}{\sqrt3}~\text V\) |
Subtopic: Â Electric Potential |
Level 3: 35%-60%
Hints
Two identical thin non-conducting spherical shells of radius \(r\) are charged uniformly with equal and opposite charges \(+Q,-Q\) and placed, so that their surfaces almost touch each other, externally (see figure). The electric fields at their centres are \(\vec E_A,\vec E_B\) while the potentials are \(V_A,V_B\) respectively. Then:
1. \(\vec E_A=\vec E_B,V_A=V_B\)
2. \(\vec E_A=-\vec E_B,V_A=V_B\)
3. \(\vec E_A=\vec E_B,V_A=-V_B\)
4. \(\vec E_A=-\vec E_B,V_A=-V_B\)
1. \(\vec E_A=\vec E_B,V_A=V_B\)
2. \(\vec E_A=-\vec E_B,V_A=V_B\)
3. \(\vec E_A=\vec E_B,V_A=-V_B\)
4. \(\vec E_A=-\vec E_B,V_A=-V_B\)
Subtopic: Â Electric Potential |
Level 3: 35%-60%
Hints
A pair of parallel metallic plates having a surface area \(A\) (each), facing each other, are placed with a small separation \(d\) between them. The two plates \(\mathrm{(I, II)}\) are given different charges and their potentials \(V_{\mathrm I},V_{\mathrm{II}}\) are measured.
If plate \(\mathrm I\) is given a charge \(+Q\) and plate \(\mathrm{II}\) is given \(-Q,\) then \(V_{\mathrm{I}}=\)
1. \({\Large\frac{Qd}{A\varepsilon_0}}\)
2. \({\Large\frac{Qd}{2A\varepsilon_0}}\)
3. \({\Large\frac{2Qd}{A\varepsilon_0}}\)
4. \({\Large\frac{Qd}{4A\varepsilon_0}}\)
If plate \(\mathrm I\) is given a charge \(+Q\) and plate \(\mathrm{II}\) is given \(-Q,\) then \(V_{\mathrm{I}}=\)
1. \({\Large\frac{Qd}{A\varepsilon_0}}\)
2. \({\Large\frac{Qd}{2A\varepsilon_0}}\)
3. \({\Large\frac{2Qd}{A\varepsilon_0}}\)
4. \({\Large\frac{Qd}{4A\varepsilon_0}}\)
Subtopic: Â Electric Potential |
 60%
Level 2: 60%+
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