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The figure shows a 2.0 V potentiometer used for the determination of the internal resistance of a 1.5 V cell. The balance point of the cell in the open circuit is 76.3 cm. When a resistor of 9.5 Ω is used in the external circuit of the cell, the balance point shifts to 64.8 cm length of the potentiometer wire. The internal resistance of the cell is:
The electrostatic force on a small sphere of charge $0.4 \, \mu\text{C}$ due to another small sphere of charge $-0.8 \, \mu\text{C}$ in the air is $0.2 \, \text{N}$. The distance between the two spheres is:
A long solenoid has 500 turns. When a current of $2 \text{ A}$ is passed through it, the resulting magnetic flux linked with each turn of the solenoid is $4 \times 10^{-3} \text{ Wb}$. The self-inductance of the solenoid is:
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:
The magnetic potential energy stored in a certain inductor is $25 \text{ mJ}$, when the current in the inductor is $60 \text{ mA}$. This inductor is of inductance:
The current ($I$) in the inductance is varying with time ($t$) according to the plot shown in the figure. Which one of the following is the correct variation of voltage with time in the coil?
The equivalent capacitance of the combination shown in the figure is:
When light propagates through a material medium of relative permittivity, $\varepsilon_r$ and relative permeability, $\mu_r$, the velocity of light, $v$ is given by: ($c$ = velocity of light in vacuum)
Three point charges +q, -2q and +q are placed at points (x=0, y=a, z=0), (x=0, y=0, z=0) and (x=a, y=0, z=0) respectively. The magnitude and direction of the electric dipole moment vector of this charge assembly are:
A toy car with charge q moves on a frictionless horizontal plane surface under the influence of a uniform electric field E. Due to the force qE, its velocity increases from 0 to 6 m/s in a one-second duration. At that instant, the direction of the field is reversed. The car continues to move for two more seconds under the influence of this field. The average velocity and the average speed of the toy car between 0 to 3 seconds are respectively:
A parallel plate air capacitor has capacitance $C$, the distance of separation between plates is $d$ and potential difference $V$ is applied between the plates. The force of attraction between the plates of the parallel plate air capacitor is:
The electric and magnetic fields of an electromagnetic wave are:
A circular disc of the radius $0.2 \text{ m}$ is placed in a uniform magnetic field of induction $\frac{1}{\pi} \text{ Wb m}^{-2}$ in such a way that its axis makes an angle of $60^\circ$ with $\vec{B}$. The magnetic flux linked to the disc will be:
Two identical charged spheres suspended from a common point by two massless strings of lengths l are initially at a distance d (d << l) apart because of their mutual repulsion. The charges begin to leak from both the spheres at a constant rate. As a result, the spheres approach each other with a velocity v. Then v varies as a function of the distance x between the spheres, as:
A system has two charges, q_A = 2.5 × 10⁻⁷ C and q_B = -2.5 × 10⁻⁷ C, located at points A: (0, 0, -15 cm) and B: (0, 0, +15 cm) respectively. The electric dipole moment of the system is:
Four point charges $q_A = 2 \mu\text{C}$, $q_B = -5 \mu\text{C}$, $q_C = 2 \mu\text{C}$, and $q_D = -5 \mu\text{C}$ are located at the corners of a square ABCD of side 10 cm. The force on a charge of $1 \mu\text{C}$ placed at the centre of the square is:
The magnetic energy stored in an inductor of inductance $4 \text{ }\mu\text{H}$ carrying a current of $2 \text{ A}$ is:
A capacitor of 2 μF is charged as shown in the figure. When the switch S is turned to position 2, the percentage of its stored energy dissipated is:
If $R$ is the radius of the earth and $g$ is the acceleration due to gravity on the earth surface. Then the mean density of the earth will be:
The diagrams below show regions of equipotentials. A positive charge is moved from A to B in each diagram. Then: