Q. No.
| 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. | \(\dfrac{-q^2}{4\pi\varepsilon_0d}\Big(6-\dfrac{1}{\sqrt2}\Big)\) |
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. | \(\dfrac{r}{8}\) |
| 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). |
( 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. | \(3 \times 10^5\) |
| 1. | \(\dfrac{rV}{R^2}\) | 2. | \(\dfrac{R^2V}{r^3}\) |
| 3. | \(\dfrac{RV}{r^2}\) | 4. | \(\dfrac{V}{r}\) |
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. \(1320~\text{V}\)
| 1. |  |
2. |  |
| 3. |  |
4. |  |
| 1. | \(180^\circ\) | 2. | \(0^\circ\) |
| 3. | \(45^\circ\) | 4. | \(90^\circ\) |
The diagrams below show regions of equipotential.
A positive charge is moved from \(A\) to \(B\) in each diagram. Choose the correct statement from the options given below:
| 1. | in all four cases, the work done is the same. |
| 2. | minimum work is required to move \(q\) in figure \(\mathrm{(a)}.\) |
| 3. | maximum work is required to move \(q\) in figure \(\mathrm{(b)}.\) |
| 4. | maximum work is required to move \(q\) in figure \(\mathrm{(c)}.\) |
In a certain region of space with volume \(0.2~\text m^3,\) the electric potential is found to be \(5~\text V\) throughout. The magnitude of the electric field in this region is:
| 1. | \(0.5~\text {N/C}\) | 2. | \(1~\text {N/C}\) |
| 3. | \(5~\text {N/C}\) | 4. | zero |
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