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Two pith balls carrying equal charges are suspended from a common point by strings of equal length, the equilibrium separation between them is r. Now the strings are rigidly clamped at half the height. The equilibrium separation between the balls now becomes:
A conducting square frame of side $a$ and a long straight wire carrying current $I$ are located in the same plane as shown in the figure. The frame moves to the right with a constant velocity $v$. The emf induced in the frame will be proportional to:
Two astronauts are floating in a gravity free space after having lost contact with their spaceship. The two will:
An emf is generated by an ac generator having 100 turn coil, of loop area 1 m². The coil rotates at a speed of one revolution per second and placed in a uniform magnetic field of 0.05 T perpendicular to the axis of rotation of the coil. The maximum value of emf is:
A thin conducting ring of 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:
A parallel-plate capacitor of area A, plate separation d, and capacitance C is filled with four dielectric materials having dielectric constants k₁, k₂, k₃ and k₄ as shown in the figure below. If a single dielectric material is to be used to have the same capacitance C in this capacitor, then its dielectric constant k is given by:
One mole of an ideal diatomic gas undergoes a transition from A to B along a path AB as shown in the figure. The change in internal energy of the gas during the transition is:
Which colour of the light has the longest wavelength?
The magnetic field of a plane electromagnetic wave is given by, $\vec B=3\times10^{-8}\cos(1.6\times10^3x+48\times10^{10}t)\hat j \text{ T}$. The associated electric field will be:
A point charge causes an electric flux of $-1.0 \times 10^3$ Nm$^2$/C to pass through a spherical Gaussian surface of 10.0 cm radius centered on the charge. If the radius of the Gaussian surface were doubled, how much flux would pass through the surface?
For a plane electromagnetic wave propagating in the $x$-direction, which one of the following combinations gives the correct possible directions for the electric field ($\mathbf{E}$) and magnetic field ($\mathbf{B}$) respectively?
The figure below shows tracks of three charged particles in a uniform electrostatic field. Which particle has the highest charge to the mass ratio?
The electric potential at a point $(x, y, z)$ is given by $V = -x^2y - xz^3 + 4$. The electric field $\vec{E}$ at that point is:
A point charge of $2.0 \, \mu\text{C}$ is at the center of a cubic Gaussian surface $9.0 \, \text{cm}$ on edge. What is the net electric flux through the surface?
The electric field associated with an electromagnetic wave in vacuum is given by $E = 40 \cos(kz - 6 \times 10^8 t)$, where $E$, $z$, and $t$ are in volt/m, meter, and second respectively. The value of the wave vector $k$ would be:
Which of the following statements is false for the properties of electromagnetic waves?
An ideal inductor-resistor-battery circuit is switched on at $t=0$ s. At time $t$, the current is $i=i_0(1-e^{-t/\tau})$, where $i_0$ is the steady-state value. The time at which the current becomes $0.5i_0$ is: [Given $\ln(2)=0.693$]
If $\vec{E}$ and $\vec{B}$ represent the electric field vector and magnetic field vector, respectively, in an electromagnetic wave then the direction of EM wave is along:
The velocity of electromagnetic radiation in a medium of permittivity $\varepsilon_0$ and permeability $\mu_0$ is given by:
In a plane electromagnetic wave travelling in free space, the electric field component oscillates sinusoidally at a frequency of $2.0 \times 10^{10} \text{ Hz}$ and amplitude $48 \text{ V m}^{-1}$. Then the amplitude of the oscillating magnetic field is: (Speed of light in free space $= 3 \times 10^8 \text{ m s}^{-1}$)