Electrostatic Potential and Capacitance

A combination of capacitors is set up as shown in the figure. The magnitude of the electric field, due to a point charge Q (having a charge equal to the sum of the charges on the 4 µF and 9 µF capacitors), at a point distant 30 m from it, would equal:

• 240N/C

• 360N/C

• 420N/C

• 420N/C

A uniformly charged solid sphere of radius R has potential V0 (measured with respect to ∞) on its surface. For this sphere, the equipotential surfaces with potentials 3Vo/2, 5Vo/4, 3V/4 and Vo/4 have radius R₁, R₂,R₃ and R4 respectively. Then

• R₁ = 0 and R₂>(R₄-R₃)

• R₁≠0 and (R₂-R₁)>(R₄-R₃)

• R₁ = 0 and R₂<(R₄-R₃)

• R₁ = 0 and R₂<(R₄-R₃)

In the given circuit, charge Q2 on the 2 μF capacitor changes as C is varied from 1 μF to 3 μF.  Q₂ as a function of ‘C’ is given properly by : (figures are drawn schematically and are not to scale)

Assume that an electric field  exists in space. Then the potential difference V_A – V_O, where VO is the potential at the origin and V_A the potential at x = 2 m is:

• 120 J

• -120 J

• -80 J

• -80 J

A parallel plate capacitor is made of two circular plates separated by a distance of 5 mm and with a dielectric of dielectric constant 2.2 between them. When the electric field in the dielectric is 3 × 104 V/m, the charge density of the positive plate will be close to

• 6 x 10^-7 C/m²

• 3  x 10^-7 C/m²

• 3 x 10⁴ C/m²

• 3 x 10⁴ C/m²

Two capacitors C₁ and C₂ are charged to 120 V and 200 V respectively. It is found that by connecting them together the potential on each one can be made zero. Then

• 5C₁ = 3C₂

• 3C₁ = 5C₂

• 3C₁ = 5C₂ = 0

• 3C₁ = 5C₂ = 0

The figure shows an experimental plot for discharging of a capacitor in an R-C circuit. The time constant τ of this circuit lies between

• 150 sec and 200 sec

• 0 and 50 sec

• 50 sec and 100 sec

• 50 sec and 100 sec

A fully charged capacitor C with initial charge q₀ is connected to a coil of self inductance L at t = 0. The time at which the energy is stored equally between the electric and the magnetic fields is

The electrostatic potential inside a charged spherical ball is given by Φ = ar² + b where r is the distance from the centre; a,b are constants. Then the charge density inside the ball is

• -6aε₀r

• -24πaε₀

• -6aε₀

• -6aε₀

Let C be the capacitance of a capacitor discharging through a resistor R. Suppose t₁ is the time taken for the energy stored in the capacitor to reduce to half its initial value and t₂ is the time taken for the charge to reduce to one–fourth its initial value. Then the ratio t₁/t₂ will be

• 1

• 1/2

• 1/4

• 1/4