Q. No.| 1. | \(0.125\times10^{-3}~\text{C m}^{-2}\) | 2. | \(0.25\times10^{-3}~\text{C m}^{-2}\) |
| 3. | \(4\times10^{-3}~\text{C m}^{-2}\) | 4. | \(0.4\times10^{-3}~\text{C m}^{-2}\) |
| 1. | \(\dfrac{F}{2}\) | 2. | \(\dfrac{3 F}{8}\) |
| 3. | \(\dfrac{3 F}{5}\) | 4. | \(\dfrac{2 F}{3}\) |
(Given that the charge of the proton and electron each \(=1.6\times 10^{-19},\) the mass of the electron \(=9.11\times 10^{-31}~\text{kg},\) the mass of the proton \(=1.67\times 10^{-27}~\text{kg}\) )
| 1. | \(10^{20}\) | 2. | \(10^{30}\) |
| 3. | \(10^{40}\) | 4. | \(10\) |
| 1. | \(\dfrac{-Q}{4}\) | 2. | \(\dfrac{Q}{4}\) |
| 3. | \(\dfrac{-Q}{2}\) | 4. | \(\dfrac{Q}{2}\) |
| 1. | \(\dfrac{r}{\sqrt[3]{2}}\) | 2. | \(\dfrac{r}{\sqrt[2]{2}}\) |
| 3. | \(\dfrac{2r}{3}\) | 4. | none of the above |
Twelve point charges each of charge \(q~\text C\) are placed at the circumference of a circle of radius \(r~\text{m}\) with equal angular spacing. If one of the charges is removed, the net electric field (in \(\text{N/C}\)) at the centre of the circle is:
(\(\varepsilon_0\text- \)permittivity of free space)
| 1. | \(\dfrac{13q}{4\pi \varepsilon_0r^2}\) | 2. | zero |
| 3. | \(\dfrac{q}{4\pi \varepsilon_0r^2}\) | 4. | \(\dfrac{12q}{4\pi \varepsilon_0r^2}\) |
A hollow metal sphere of radius \(R\) is uniformly charged. The electric field due to the sphere at a distance \(r\) from the centre:
| 1. | decreases as \(r\) increases for \(r<R\) and for \(r>R\). |
| 2. | increases as \(r\) increases for \(r<R\) and for \(r>R\). |
| 3. | is zero as \(r\) increases for \(r<R\), decreases as \(r\) increases for \(r>R\). |
| 4. | is zero as \(r\) increases for \(r<R\), increases as \(r\) increases for \(r>R\). |
An electron falls from rest through a vertical distance \(h\) in a uniform and vertically upward-directed electric field \(E\). The direction of the electric field is now reversed, keeping its magnitude the same. A proton is allowed to fall from rest through the same vertical distance \(h\). The fall time of the electron in comparison to the fall time of the proton is:
| 1. | smaller | 2. | \(5\) times greater |
| 3. | \(10\) times greater | 4. | equal |
A toy car with charge \(q\) moves on a frictionless horizontal plane surface under the influence of a uniform electric field \(\vec {E}.\) Due to the force \(q\vec {E},\) its velocity increases from \(0\) to \(6~\text{m/s}\) in a one-second duration. At that instant, the direction of the field is reversed. The car continues to move for two more seconds under the influence of this field. The average velocity and the average speed of the toy car between \(0\) to \(3\) seconds are respectively:
| 1. | \(2~\text{m/s}, ~4~\text{m/s}\) | 2. | \(1~\text{m/s}, ~3~\text{m/s}\) |
| 3. | \(1~\text{m/s}, ~3.5~\text{m/s}\) | 4. | \(1.5~\text{m/s},~ 3~\text{m/s}\) |
| 1. | \(2~\text{mC}\) | 2. | \(8~\text{mC}\) |
| 3. | \(6~\text{mC}\) | 4. | \(4~\text{mC}\) |
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