A thin spherical shell of radius R and surface charge density \(\sigma\) is placed in a cube of side 5 R with their centers coinciding. The electric flux through one face of the cube is \(\left(\varepsilon_0=\right.\) Permittivity of free space \()\)

A straight conductor of length \(4 \mathrm{~m}\) moves at a speed of \(10 \mathrm{~m} / \mathrm{s}\). When the conductor makes on angle of \(30^{\circ}\) with the direction of magnetic field of induction of \(0.1 \mathrm{~Wb}-\mathrm{m}^2\), then induced emf is

An energy of \(13.6 \mathrm{eV}\) is equal to

A cell of emf \(10 \mathrm{~V}\) and internal resistance \(3 \Omega\) is connected in parallel with another cell of emf \(7 \mathrm{~V}\) and internal resistance \(\frac{3}{5} \Omega\), such that their positive terminals are joined together and so their are negative terminals. Their positive terminals are joined with the negative terminal and their negative terminal is joined with the positive terminal of a third cell of emf \(20 \mathrm{~V}\) with internal resistance \(2 \Omega\). The combination can be replaced by a battery of emf \(E\) and internal resistance \(r\), then the values of \(E\) and \(R\) are respectively

An inductance \(1 \mathrm{H}\) is connected in series with an AC source of \(220 \mathrm{~V}\) and \(50 \mathrm{~Hz}\). The. inductive reactance (in ohm) is

A copper ball of radius \(3.0 \mathrm{~mm}\) falls in an oil tank of viscosity \(1 \mathrm{~kg} / \mathrm{ms}\). Then, the terminal velocity of the copper ball will be (Density of oil \(=1.5 \times 10^3 \mathrm{~kg} / \mathrm{m}^3\), Density of copper \(=9 \times 10^3 \mathrm{~kg} / \mathrm{m}^3\) and \(g=10 \mathrm{~m} / \mathrm{s}^2\).)

A coil is connected to an AC source with peak emf, \(8 \mathrm{~V}\) and frequency \(\frac{30}{\pi} \mathrm{Hz}\). The coil has resistance of \(8 \Omega\). If the average power dissipated by the coil is \(0.4 \mathrm{~W}\), then the inductance of the coil is

For any fixed distance, the electromagnetic force between two protons is \(10^n\) times of the gravitational force between them. Then \(\mathrm{n}=\)

A body is projected from the ground at an angle of \(\tan ^{-1}(\sqrt{7})\) with the horizontal. At half of the maximum height, the speed of the body is ' \(n\) ' times the speed of projection. The value of ' \(n\) ' is

In a meter bridge experiment the ratio of the left gap resistance to the right gap resistance is \(2: 3\). The balance length from left end is

A wire of length, $l$ carries a current $I$ along the $X$- axis. The magnetic force acting on the wire is given by $\overrightarrow{F}=I{B}_{0}L(\hat{\mathrm{k}}-\hat{\mathrm{j}})\mathrm{T}$ where $B_0$ is a constant. The existing magnetic field $\overrightarrow{B}$ is

Photons of energy 4.5 eV are incident on a photosensitive material of work function 3 eV. The de Broglie wavelength associated with the photoelectrons emitted with maximum kinetic energy is nearly

If \(\lambda_0\) is the de-Broglie wavelength for a proton accelerated through a potential difference of \(100 \mathrm{~V}\), the de-Broglie wavelength for \(\alpha\)-particle accelerated through the same potential difference is