List of top Questions asked in JEE Main

A sinusoidal electromagnetic wave is given by \( \vec{E} = 20 \sin \left( \frac{2}{300} x - 10^6 t \right) \) propagating in a non-magnetic material. Dielectric constant of the material is.
If electric field component is $E = 377\sin(\omega t + kx)$ V/m of an electromagnetic wave and \[ \sqrt{\frac{\mu_0}{\varepsilon_0}} = 377, \] then find the average intensity of the wave (in W/m$^2$):
Dielectric constant of a medium is 3 and its magnetic permeability \(\mu = 2\mu_0\). Find ratio of velocity of light in vacuum to velocity of light in medium :
Following are two lists, list-I contains the types of electromagnetic waves and list-II contains theirs source. Match the entries from list-I to appropriate entries from list-II.
Equation of an electromagnetic wave in a medium is given by \[ E = 2\sin\left(2\times 10^{15}t - 10^{7}x\right). \] Find the refractive index of the medium.
An electromagnetic wave travelling in a medium has its electric field given by : \(E = 2\sin(2 \times 10^{15}t - 10^7x)\). Find the refractive index of the medium :
Consider the following electromagnetic waves: wave A :- wavelength = \(400\,\text{nm}\)
wave B :- frequency = \(10^{16}\,\text{Hz}\)
wave C :- wave number = \(10^{4}\,\text{cm}^{-1}\)
order of energy is :
Electric field of an EM wave is given as \(\vec{E} = 54\sin(kz-\omega t)\,\hat{i}\). Then what will be its corresponding magnetic field?
Escape velocity from a planet of radius \(R\) and density \(\rho\) is given as \(10\,\text{km s}^{-1}\). Find the escape velocity from a planet of radius \(\dfrac{R}{10}\) and density \(\dfrac{\rho}{10}\).
If initially the force on \(m_0\) is \(F_0\). When the positions of \(4m\) and \(3m\) are interchanged, the force becomes \(F'\). If \[ \frac{F_0}{F'}=\frac{\alpha}{\sqrt{5}}, \] find \(\alpha\).
A planet 'A' having density \( \rho \) and radius \( R \) has escape velocity \( = 10 \, \text{km/sec} \). Find the escape velocity of a planet B having density and radius both 10% that of planet A.
For an object revolving around a planet of mass \( M \) and radius \( R_0 \) at a distance \( r \) from the center of the planet. If area velocity of the object is 10 km/sec. Now if the density of the planet increases by +10% and radius of the planet increases by +10%, then find the new area velocity at the same orbital radius.
A satellite is revolving around a planet in orbit radius of 1.5 R. Additional minimum energy required to transfer the satellite to the new orbit radius of 3R is (G and M are mass of satellite \& planet)
If a satellite orbiting the Earth is 9 times closer to the Earth than the Moon, what is the time period of rotation of the satellite? Given rotational time period of Moon = 27 days and gravitational attraction between the satellite and the Moon is neglected.
Three masses m\(_{1}\) = 200 kg, m\(_{2}\) = 300 kg and m\(_{3}\) = 400 kg are kept at the vertices of on equilateral triangle of side 20 m. If the masses are shifted to new configuration such that they are at the vertices of an equilateral triangle of 25 m now. Find the work done in this process :
An \( \alpha \)-particle having kinetic energy \(7.7\,\text{MeV}\) is approaching a fixed gold nucleus (atomic number \(Z = 79\)). Find the distance of closest approach.
An air-filled capacitor of capacitance \( C \) is filled with a dielectric (\( k = 3 \)) of width \( \frac{d}{3} \), where \( d \) is the separation between the plates. The new capacitance is:
An $\alpha$-particle having kinetic energy $7.7$ MeV is approaching a fixed gold nucleus (atomic number is 79). Find the distance of closest approach.
Find out work done in moving a $2\,\mu$C charge from point $A$ to $B$.
Two spheres having equal mass \(m\), charge \(q\), and radius \(R\) are moving towards each other. Both have speed \(u\) at an instant when the distance between their centres is \(4R\). Find the minimum value of \(u\) so that they just touch each other.
A simple pendulum with bob (mass $m$ and charge $q$) is in equilibrium in the presence of a horizontal electric field $E$. Then the tension in the thread is:
Find electric field intensity \( \vec{E} \) at the centre of the circle shown in the figure.
A simple pendulum with bob of mass \(m\) carrying charge \(q\) is in equilibrium in the presence of a horizontal electric field \(E\). Then the tension in the thread is:
If the electric potential is \(V = 500\) volts at the point \((10,\,20)\) and the electric field is given by \[ \vec{E} = 10x\,\hat{i} + 5y\,\hat{j}\ \text{N/C}, \] find the potential at the origin.
There are two point charges, one at the vertex and the other at the face of a cube as shown. Find the electric flux through the cube.