An electron is moving in a circular path under the influence of a transverse magnetic field of 3.57 × 10^–2 T. If the value of e/m is 1.76 × 10¹¹ C/kg, the frequency of revolution of the electron is :

A bar magnet is hung by a thin cotton thread in a uniform horizontal magnetic field and is in equilibrium state. The energy required to rotate it by 60º is W. Now the torque required to keep the magnet in this new position is :

A long wire carrying a steady current is bent into a circular loop of one turn. The magnetic field at the centre of the loop is B. It is then bent into a circular coil of n turns. The magnetic field at the centre of this coil of n turns will be :

A filament bulb (500 W, 100 V) is to be used in a 230 V main suply. When a resistance R is connected in series, it works perfectly and the bulb consumes 500 W. The value of R is : 

The potential difference (V_A – V_B) between the points A and B in the given figure is :

A parallel- plate capacitor of area A, plate separation d and capacitance C is filled with four dielectric materials having dielectric constant 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