1. | \(\frac{rV}{R^2}\) | 2. | \(\frac{R^2V}{r^3}\) |
3. | \(\frac{RV}{r^2}\) | 4. | \(\frac{V}{r}\) |
1. | dependent on the material property of the sphere |
2. | more on bigger sphere |
3. | more on smaller sphere |
4. | equal on both the spheres |
A hollow metal sphere of radius \(R\) is given \(+Q\) charges to its outer surface. The electric potential at a distance \(\frac{R}{3}\) from the centre of the sphere will be:
1. \(\frac{1}{4\pi \varepsilon_0}\frac{Q}{9R}\)
2. \(\frac{3}{4\pi \varepsilon_0}\frac{Q}{R}\)
3. \(\frac{1}{4\pi \varepsilon_0}\frac{Q}{3R}\)
4. \(\frac{1}{4\pi \varepsilon_0}\frac{Q}{R}\)
Two charged spherical conductors of radii \(R_1\) and \(R_2\) are connected by a wire. The ratio of surface charge densities of spheres \(\left ( \frac{\sigma _{1}}{\sigma _{2}}\right )\) is:
1. \(\sqrt{\frac{R_1}{R_2}}\)
2. \(\frac{R^2_1}{R^2_2}\)
3. \(\frac{R_1}{R_2}\)
4. \(\frac{R_2}{R_1}\)
Twenty seven drops of same size are charged at \(220~\text{V}\) each. They combine to form a bigger drop. Calculate the potential of the bigger drop.
1. \(1520~\text{V}\)
2. \(1980~\text{V}\)
3. \(660~\text{V}\)
4. \(1320~\text{V}\)
The variation of electrostatic potential with radial distance \(r\) from the centre of a positively charged metallic thin shell of radius \(R\) is given by the graph:
1. | 2. | ||
3. | 4. |
A conducting sphere of the radius \(R\) is given a charge \(Q.\) The electric potential and the electric field at the centre of the sphere respectively are:
1. | \(\frac{Q}{4 \pi \varepsilon_0 {R}^2}\) | zero and2. | \(\frac{Q}{4 \pi \varepsilon_0 R}\) and zero |
3. | \(\frac{Q}{4 \pi \varepsilon_0 R}\) and \(\frac{Q}{4 \pi \varepsilon_0{R}^2}\) | 4. | both are zero |
Four-point charges \(-Q, -q, 2q~\text{and}~2Q\) are placed, one at each corner of the square. The relation between \(Q\) and \(q\) for which the potential at the center of the square is zero is:
1. | \(Q= -q\) | 2. | \(Q= -2q\) |
3. | \(Q= q\) | 4. | \(Q= 2q\) |
Two metallic spheres of radii \(1~\text{cm}\) and \(3~\text{cm}\) are given charges of \(-1\times 10^{-2}~\text{C}\) and \(5\times 10^{-2} ~\text{C}\), respectively. If these are connected by a conducting wire, then the final charge on the bigger sphere is:
1. \(3\times 10^{-2}~ \text{C}\)
2. \(4\times 10^{-2}~\text{C}\)
3. \(1\times 10^{-2}~\text{C}\)
4. \(2\times 10^{-2}~\text{C}\)