In a certain region of space, the electric field is along the z-direction throughout. The magnitude of the electric field is, however, not constant but increases uniformly along the positive z-direction, at the rate of 105 NC-1 per meter. What is the torque experienced by a system having a total dipole moment equal to in the negative z-direction?
1. | 2. | ||
3. | 4. |
A spherical conducting shell of inner radius and outer radius has a charge Q. A charge q is placed at the center of the shell. The surface charge density on the outer surfaces of the shell is:
1. | \(\frac{Q+q}{4 \pi r_{2}^{2}}\) | 2. | \(\frac{q}{4 \pi r_{1}^{2}}\) |
3. | \(\frac{-Q+q}{4 \pi r_{2}^{2}}\) | 4. | \(\frac{-q}{4 \pi r_{1}^{2}}\) |
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 \(r>R\). |
Point charges +4q, –q and +4q are kept on the x-axis at points x = 0, x = a and x = 2a respectively, then:
1. | Only -q is in stable equilibrium. |
2. | None of the charges are in equilibrium. |
3. | All the charges are in unstable equilibrium. |
4. | All the charges are in stable equilibrium. |
A particle of mass m carrying charge -q1 is moving around a charge +q2 along a circular path of radius r. The period of revolution of the charge -q1 is:
1.
2.
3.
4. zero
A polythene piece rubbed with wool is found to have a negative charge of . Transfer of mass from wool to polythene is:
1. 0.7 × 10 - 18 kg
2. 1.7 × 10 - 17 kg
3. 0.7 × 10 - 17 kg
4. 1.7 × 10 - 18 kg
Two point dipoles of dipole moment and are at a distance x from each other and . The force between the dipole is:
1.
2.
3.
4.
A spherical conductor of radius \(10~\text{cm}\) has a charge of \(3.2 \times 10^{-7}~\text{C}\) distributed uniformly. What is the magnitude of the electric field at a point \(15~\text{cm}\) from the center of the sphere? \(\frac{1}{4\pi \varepsilon _0} = 9\times 10^9~\text{N-m}^2/\text{C}^2\)
1. \(1.28\times 10^{5}~\text{N/C}\)
2. \(1.28\times 10^{6}~\text{N/C}\)
3. \(1.28\times 10^{7}~\text{N/C}\)
4. \(1.28\times 10^{4}~\text{N/C}\)
If there were only one type of charge in the universe, then,
1. | on any surface. |
2. | if the charge is outside the surface. |
3. | could not be defined. |
4. | if charges of magnitude q were inside the surface. |
Consider a region inside where there are various types of charges but the total charge is zero. At points outside the region:
a. | the electric field is necessarily zero. |
b. | the electric field is due to the dipole moment of the charge distribution only. |
c. | the dominant electric field is for large r, where r is the distance from the origin in this region. |
d. | the work done to move a charged particle along a closed path, away from the region, will be zero. |
Which of the above statements are true?
1. b and d
2. a and c
3. b and c
4. c and d