List of top Questions asked in JEE Main

A coil of area A and N turns is rotating with angular velocity $ \omega$ in a uniform magnetic field $\vec{B}$ about an axis perpendicular to $ \vec{B}$ Magnetic flux $\varphi \text{ and induced emf } \varepsilon \text{ across it, at an instant when } \vec{B} \text{ is parallel to the plane of the coil, are:}$

Consider a long straight wire of a circular cross-section (radius $ a $) carrying a steady current $ I $. The current is uniformly distributed across this cross-section. The distances from the center of the wire's cross-section at which the magnetic field (inside the wire, outside the wire) is half of the maximum possible magnetic field, anywhere due to the wire, will be:

A rectangular metallic loop is moving out of a uniform magnetic field region to a field-free region with a constant speed. When the loop is partially inside the magnetic field, the plot of the magnitude of the induced emf $ (\varepsilon) $ with time $ (t) $ is given by: \includegraphics[width=1\linewidth]{3.png}

If $ \epsilon_0 $ denotes the permittivity of free space and $ \Phi_E $ is the flux of the electric field through the area bounded by the closed surface, then the dimension of $ \epsilon_0 \frac{d\Phi_E}{dt} $ are that of:

Conductor wire ABCDE with each arm 10 cm in length is placed in magnetic field of $\frac{1}{\sqrt{2}}$ Tesla, perpendicular to its plane. When conductor is pulled towards right with constant velocity of $10 \mathrm{~cm} / \mathrm{s}$, induced emf between points A and E is _______ mV.}

Match List - I with List - II:

List - I:

(A) Electric field inside (distance $ r > 0 $ from center) of a uniformly charged spherical shell with surface charge density $ \sigma $, and radius $ R $.
(B) Electric field at distance $ r > 0 $ from a uniformly charged infinite plane sheet with surface charge density $ \sigma $.
(C) Electric field outside (distance $ r > 0 $ from center) of a uniformly charged spherical shell with surface charge density $ \sigma $, and radius $ R $.
(D) Electric field between two oppositely charged infinite plane parallel sheets with uniform surface charge density $ \sigma $.

List - II:

(I) $ \frac{\sigma}{\epsilon_0} $
(II) $ \frac{\sigma}{2\epsilon_0} $
(III) 0
(IV) $ \frac{\sigma}{\epsilon_0 r^2} $ Choose the correct answer from the options given below:

An electric dipole is placed at a distance of 2 cm from an infinite plane sheet having positive charge density $ \sigma $. Choose the correct option from the following.

The electrostatic potential on the surface of a uniformly charged spherical shell of radius $ R = 10 \, \text{cm} $ is 120 V. The potential at the centre of the shell, at a distance 5 cm from the centre, and at a distance 15 cm from the centre of the shell are:

There are two charged spheres of radius $R$ and $3R$. When the spheres are made to touch each other and then separate, the surface charge density becomes $r_1$ and $r_2$ respectively. Find $\frac{r_1}{r_2}$.

Given $\lambda = \frac{2nc}{m}$ (linear charge density) for a wire which is passing through the body diagonal of a closed cube of side length $\sqrt{3}$ cm. Find the flux through the cube.

There are two charged spheres of radius $ R $ and $ 3R $. When the spheres are made to touch each other and then separate, the surface charge density becomes $ \sigma_1 $ and $ \sigma_2 $ respectively. Find the ratio $ \frac{\sigma_1}{\sigma_2} $.

Assertion (A): Work done to move a charge between two points is zero inside a uniformly charged shell.
Reason (R): Potential inside a uniformly charged shell is constant and equal to the potential at its surface.

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R
Assertion A: Work done in moving a test charge between two points inside a uniformly charged spherical shell is zero, no matter which path is chosen.
Reason R: Electrostatic potential inside a uniformly charged spherical shell is constant and is same as that on the surface of the shell.
In the light of the above statements, choose the correct answer from the options given below

Two metal spheres of radius $ R $ and $ 3R $ have same surface charge density $ \sigma $. If they are brought in contact and then separated, the surface charge density on smaller and bigger sphere becomes $ \sigma_1 $ and $ \sigma_2 $, respectively. The ratio $ \frac{\sigma_1}{\sigma_2} $ is:

Electric charge is transferred to an irregular metallic disk as shown in the figure. If $ \sigma_1 $, $ \sigma_2 $, $ \sigma_3 $, and $ \sigma_4 $ are charge densities at given points, then choose the correct answer from the options given below:

An electron is released from rest near an infinite non-conducting sheet of uniform charge density '–σ'. The rate of change of de-Broglie wavelength associated with the electron varies inversely as $n^{th}$ power of time. The numerical value of $n$ is ______.

Space between the plates of a parallel plate capacitor of plate area 4 cm$^2$ and separation of $ d = 1.77 \, \text{mm} $, is filled with uniform dielectric materials with dielectric constants (3 and 5) as shown in figure. Another capacitor of capacitance 7.5 pF is connected in parallel with it. The effective capacitance of this combination is ____ pF.

Three parallel plate capacitors $ C_1 $, $ C_2 $, and $ C_3 $ each of capacitance 5 µF are connected as shown in the figure. The effective capacitance between points A and B, when the space between the parallel plates of $ C_1 $ capacitor is filled with a dielectric medium having dielectric constant of 4, is:

Two charges $ q_1 $ and $ q_2 $ are separated by a distance of 30 cm. A third charge $ q_3 $ initially at C as shown in the figure, is moved along the circular path of radius 40 cm from C to D. If the difference in potential energy due to the movement of $ q_3 $ from C to D is given by $ \frac{q_3 K}{4 \pi \epsilon_0} $, the value of $ K $ is:

A parallel plate capacitor is filled equally (half) with two dielectrics of dielectric constant $ \epsilon_1 $ and $ \epsilon_2 $, as shown in figures. The distance between the plates is d and area of each plate is A. If capacitance in first configuration and second configuration are $ C_1 $ and $ C_2 $ respectively, then $ \frac{C_1}{C_2} $ is:

The electrostatic potential on the surface of uniformly charged spherical shell of radius R = 10 cm is 120 V. The potential at the centre of shell, at a distance r = 5 cm from centre, and at a distance r = 15 cm from the centre of the shell respectively, are:

Two infinite identical charged sheets and a charged spherical body of charge density ' $\rho$ ' are arranged as shown in figure. Then the correct relation between the electrical fields at $\mathrm{A}, \mathrm{B}, \mathrm{C}$ and D points is:

Two small spherical balls of mass 10 g each with charges $-2 \mu \mathrm{C}$ and $2 \mu \mathrm{C}$, are attached to two ends of very light rigid rod of length 20 cm. The arrangement is now placed near an infinite nonconducting charge sheet with uniform charge density of $100 \mu \mathrm{C} / \mathrm{m}^{2}$ such that length of rod makes an angle of $30^{\circ}$ with electric field generated by charge sheet. Net torque acting on the rod is:

Four capacitors each of capacitance $16\,\mu F$ are connected as shown in the figure. The capacitance between points A and B is __ (in $\mu F$)

Using a battery, a 100 pF capacitor is charged to 60 V and then the battery is removed. After that, a second uncharged capacitor is connected to the first capacitor in parallel. If the final voltage across the second capacitor is 20 V, its capacitance is : (in pF)