Two equal charges q of opposite sign separated by a distance 2a constitute an electric dipole of dipole moment p. If P is a point at a distance r from the centre of the dipole and the line joining the centre of the dipole to this point makes an angle θ with the axis of the dipole, then the potential at P is given by: (r >> 2a) (Where p = 2qa)
1. | \(V={pcos \theta \over 4 \pi \varepsilon_0r^2}\) | 2. | \(V={pcos \theta \over 4 \pi \varepsilon_0r}\) |
3. | \(V={psin \theta \over 4 \pi \varepsilon_0r}\) | 4. | \(V={pcos \theta \over 2 \pi \varepsilon_0r^2}\) |
Two thin dielectric slabs of dielectric constants K1&K2 () are inserted between plates of a parallel capacitor, as shown in the figure. The variation of electric field E between the plates with distance d as measured from plate P is correctly shown by:
1. | 2. | ||
3. | 4. |
A conducting sphere of radius R is given a charge Q. The electric potential and field at the center of the sphere respectively are:
1. | Zero and \(\mathrm{Q} / 4 \pi \varepsilon_{\mathrm{o}} \mathrm{R}^2\) |
2. | \(\mathrm{Q} / 4 \pi \varepsilon_{\mathrm{O}} \mathrm{R}\) and zero |
3. | \(\mathrm{Q} / 4 \pi \varepsilon_{\mathrm{O}} \mathrm{R}\) and \(\mathrm{Q} / 4 \pi \varepsilon_{\mathrm{o}} \mathrm{R}^2\) |
4. | Both are zero |
An electric dipole of moment \(p\) is placed in an electric field of intensity \(E\). The dipole acquires a position such that the axis of the dipole makes an angle \(\theta\) with the direction of the field. Assuming that the potential energy of the dipole to be zero when \(\theta = 90^{\circ},\) the torque and the potential energy of the dipole will respectively be:
1. | \(p E \sin \theta,-p E \cos \theta\) | 2. | \(p E \sin \theta,-2 p E \cos \theta\) |
3. | \(p E \sin \theta, 2 p E \cos \theta\) | 4. | \(p E \cos \theta,-p E \sin \theta\) |
The equivalent capacitance of the following arrangement is:
1.
2.
3.
4.
Two capacitors of capacitance \(6~\mu\text{F}\) and \(3~\mu\text{F}\) are connected in series with battery of \(30~\text{V}\). The charge on \(3~\mu\text{F}\) capacitor at a steady state is:
1. \( 3 ~\mu\text{C}\)
2. \( 1.5 ~\mu\text{C}\)
3. \( 60~\mu\text{C}\)
4. \( 900~\mu\text{C}\)
Two concentric metallic spherical shells A and B of radii a and b respectively (b>a) are arranged such that outer shell is earthed and inner shell is charged to Q. Charge on the outer surface of outer shell will be:
1.
2.
3. -Q
4. zero
The equivalent capacitance across \(A\) and \(B\) in the given figure is:
1. \( \frac{3}{2}C\)
2. \(C\)
3. \( \frac{2}{3}C\)
4. \( \frac{5}{3}C\)
Two capacitors of capacity and are charged to the same potential difference of 6 V. Now they are connected with opposite polarity as shown. After closing switches , their final potential difference becomes:
1. | \(\text{Zero} \) | 2. | \(\frac{4}{3} \mathrm{~V} \) |
3. | \(3 \mathrm{~V} \) | 4. | \(\frac{6}{5} \mathrm{~V}\) |
Which of the following statements is correct regarding electrostatics of conductors?
1. | The interior of the conductor with no cavity can have no excess charge in the static situation. |
2. | Electrostatic potential is constant throughout the volume of the conductor. |
3. | Electrostatic potential has the same value inside as that on its surface. |
4. | All of these. |