Q. No.The figure shows the electric lines of force emerging from a charged body. If the electric field at \(A\) and \(B\) are \(E_A\) and \(E_B\) respectively and if the displacement between \(A\) and \(B\) is \(r,\) then:
1. \(E_A>E_B\)
2. \(E_A<E_B\)
3. \(E_{A} = \frac{E_{B}}{r}\)
4. \(E_{A} = \frac{E_{B}}{r^{2}}\)
Three identical positive point charges, as shown are placed at the vertices of an isosceles right-angled triangle. Which of the numbered vectors coincides in direction with the electric field at the mid-point \(M\) of the hypotenuse?
1. \(1\)
2. \(2\)
3. \(3\)
4. \(4\)
A metallic solid sphere is placed in a uniform electric field. The lines of force, as shown in the figure, follow the path(s):
1. \(1\)
2. \(2\)
3. \(3\)
4. \(4\)
A thin conducting ring of the radius \(R\) is given a charge \(+Q.\) The electric field at the centre \(O\) of the ring due to the charge on the part \(AKB\) of the ring is \(E.\) The electric field at the centre due to the charge on the part \(ACDB\) of the ring is:
| 1. | \(3E\) along \(KO\) |
| 2. | \(E\) along \(OK\) |
| 3. | \(E\) along \(KO\) |
| 4. | \(3E\) along \(OK\) |
A charge \(q\) is placed in a uniform electric field \(E.\) If it is released, then the kinetic energy of the charge after travelling distance \(y\) will be:
| 1. | \(qEy\) | 2. | \(2qEy\) |
| 3. | 4. |
A charged particle \(q\) of mass \(m\) is released on the \(y\text-\)axis at \(y=a\) in an electric field \(\vec E = -4y \hat{j}.\) The speed of the particle on reaching the origin will be:
1. \(\sqrt{\frac{2 a}{m q}}\)
2. \(\frac{a}{\sqrt{m q}}\)
3. \(2 a \sqrt{\frac{q}{m}}\)
4. \(2 \sqrt{\frac{a}{m q}}\)
| Assertion (A): | Work done in moving a charge between any two points in a uniform electric field is independent of the path followed by the charge between these points. |
| Reason (R): | Electrostatic forces are non-conservative. |
| 1. | Both (A) and (R) are True and (R) is the correct explanation of (A). |
| 2. | Both (A) and (R) are True but (R) is not the correct explanation of (A). |
| 3. | (A) is True but (R) is False. |
| 4. | (A) is False but (R) is True. |
The electrostatic field due to a charged conductor just outside the conductor is:
| 1. | zero and parallel to the surface at every point inside the conductor. |
| 2. | zero and is normal to the surface at every point inside the conductor. |
| 3. | parallel to the surface at every point and zero inside the conductor. |
| 4. | normal to the surface at every point and zero inside the conductor. |
| Assertion (A): | The number of field lines drawn from a charge is proportional to the magnitude of the charge. |
| Reason (R): | The electric field at any point is proportional to the magnitude of the source charge. |
| 1. | Both (A) and (R) are True and (R) is the correct explanation of (A). |
| 2. | Both (A) and (R) are True but (R) is not the correct explanation of (A). |
| 3. | (A) is True but (R) is False. |
| 4. | Both (A) and (R) are False. |
Two-point charges \(+8q\) and \(-2q\) are located at \(x=0\) and \(x=L\) respectively. The location of a point on the \(x\text-\)axis at which the net electric field due to these two point charges is zero is:
1. \(8L\)
2. \(4L\)
3. \(2L\)
4. \(\frac{L}{4}\)
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