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A 800 turn coil of effective area $0.05 \text{ m}^2$ is kept perpendicular to a magnetic field $5 \times 10^{-5} \text{ T}$. When the plane of the coil is rotated by $90^\circ$ around any of its coplanar axis in $0.1 \text{ s}$, the emf induced in the coil 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 uniformly charged conducting sphere of 2.4 m diameter has a surface charge density of $80.0 \, \mu\text{C/m}^2$. The charge on the sphere is:

Two conducting circular loops of radii $R_1$ and $R_2$ are placed in the same plane with their centres coinciding. If $R_1 \gg R_2$, the mutual inductance $M$ between them will be directly proportional to:

A car sometimes overturns while taking a turn. When it overturns, it is:

Match List-I with List-II (the symbols carry their usual meaning). **List-I** (A) $\oint \vec{E} \cdot d\vec{A} = \frac{Q}{\varepsilon_0}$ (B) $\oint \vec{B} \cdot d\vec{A} = 0$ (C) $\oint \vec{E} \cdot d\vec{l} = -\frac{d\phi}{dt}$ (D) $\oint \vec{B} \cdot d\vec{l} = \mu_0 i_c + \mu_0 \varepsilon_0 \frac{d\phi_E}{dt}$ **List-II** (I) Ampere-Maxwell's law (II) Faraday's law (III) Gauss's law of electrostatics (IV) Gauss's law of magnetism

Two infinitely long parallel conducting plates having surface charge densities +σ and −σ respectively, are separated by a small distance. The medium between the plates is a vacuum. If ε₀ is the dielectric permittivity of vacuum, then the electric field in the region between the plates is:

A coil of self-inductance $L$ is connected in series with a bulb $B$ and an AC source. The brightness of the bulb decreases when:

$\varepsilon_0$ and $\mu_0$ are the electric permittivity and magnetic permeability of free space respectively. If the corresponding quantities of a medium are $2\varepsilon_0$ and $1.5\mu_0$ respectively, the refractive index of the medium will nearly be:

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:

Foetal ejection reflex in human female is induced by:

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 conducting sphere of radius 10 cm has an unknown charge. If the electric field, 20 cm from the centre of the sphere is $1.5 \times 10^3$ N/C and points radially inward, what is the net charge on the sphere?

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:

Meiotic division of the secondary oocyte is completed:

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:

A hollow cylinder has a charge q coulomb within it (at the geometrical centre). If ϕ is the electric flux in units of Volt-meter associated with the curved surface B, the flux linked with the plane surface A in units of volt-meter will be:

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:

At infinite dilution, equivalent conductances of $Ba^{2+}$ & $Cl^-$ ions are $127$ & $76 \text{ ohm}^{-1}\text{cm}^{-1}\text{ eq}^{-1}$ respectively. Equivalent conductance ($\text{ohm}^{-1}\text{cm}^{-1}\text{ eq}^{-1}$) of $BaCl_2$ at infinite dilution is: