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. \(1.28\times 10^{4}~\text{N/C}\)
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
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
An electric dipole is kept in a uniform electric field such that the dipole moment is not collinear with the electric field. It experiences:
1. | a force and torque. |
2. | a force but no torque. |
3. | a torque but no force. |
4. | neither a force nor a torque. |
A point charge is placed at the center of the spherical Gaussian surface. The electric flux through the surface is changed if the:
1. | sphere is replaced by a cube of the same volume. |
2. | sphere is replaced by a cube of half volume. |
3. | charge is moved off-centre in the original sphere. |
4. | charge is moved just outside the original sphere. |
Four charges are arranged at the corners of a square ABCD as shown in the figure. The force on a positive charge kept at the center of the square is:
1. | Zero |
2. | Along diagonal AC |
3. | Along diagonal BD |
4. | Perpendicular to the side AB |