An electric dipole is placed at an angle of 30° to a non-uniform electric field. The dipole will experience

• a torque only

• a translational force only in the direction of the field

• a translational force only in a direction normal to the direction of the field

• a translational force only in a direction normal to the direction of the field

Two insulating plates are both uniformly charged in such a way that the potential difference between them is V₂ −V₁ = 20 V. (i.e. plate 2 is at a higher potential). The plates are separated by d = 0.1 m and can be treated as infinitely large. An electron is released from rest on the inner surface of plate 1. What is its speed when it hits plate 2?


(e = 1.6 × 10⁻¹⁹ C, me = 9.11 × 10⁻³¹ kg)

• 32 × 10⁻¹⁹ m/s

• 2.65 × 10⁶ m/s

• 7.02 × 10¹² m/s

• 7.02 × 10¹² m/s

A fully charged capacitor has a capacitance ‘C’ it is discharged through a small coil of resistance wire embedded in a thermally insulated block of specific heat capacity ‘s’ and mass ‘m’. If the temperature of the block is raised by ‘∆T’. The potential difference V across the capacitance

A parallel plate capacitor is made by stacking n equally spaced plates connected alternatively. If the capacitance between any two adjacent plates is C then the resultant capacitance is

• (n − 1)C

• (n + 1)C

• C

• C

• 1.8 pF

• 40.5 pF

• 45 pF
• 45 pF

• 6 x 10^-7 C/m²
• 3  x 10^-7 C/m²
• 3 x 10⁴ C/m²
• 3 x 10⁴ C/m²

Three concentric metal shells A, B and C of respective radii a, b and c (a < b < c) have surface charge densities +σ, −σ and +σ respectively. The potential of shell B is :

28.

Seven identical circular planar disks, each of mass M and radius R are welded symmetrically as shown. The moment of inertia of the arrangement about the axis normal to the plane and passing through the point P is:

• $\frac{181}{2}M{R}^2$

• $\frac{19}{2}\hspace{0.17em}M{R}^2$

• $\frac{55}{2} M{R}^2$

• $\frac{73}{2}M{R}^2$

A parallel plate capacitor of capacitance 90 pF is connected to a battery of emf 20 V. If a dielectric material of dielectric constant K= 5/3 is inserted between the plates, the magnitude of the induced charge will be:

• 0.9 n C

• 1.2 n C

• 0.3 n C

• 2.4 n C

The dipole moment of a circular loop carrying a current I, is m and the magnetic field at the centre of the loop is B1. When the dipole moment is doubled by keeping the current constant, the magnetic field at the centre of the loop is B₂. The ratio B₁/B₂ is:

• $\frac{1}{\sqrt{2}}$

• 2

• $\sqrt{3}$

• $\sqrt{2}$