Write the expression for the work done on an electric dipole of the dipole moment p → in turning, it from its position of stable equilibrium to a position of unstable equilibrium in a uniform electric field E → .

Consider an electric dipole placed in a uniform electric field E → with its dipole moment p → making an angle θ with the field. Two equal and opposite forces + q E → and - q E → act on its two ends. The two forces form a couple. The torque exerted by the couple will be τ = q E × 2 a sin θ = p E sin θ where q × 2 a = p , is the dipole moment. If the dipole is rotated through a small angle d θ against the torque acting on it, then small work done is d W = τ d θ = p E sin θ d θ The total work done in rotating the dipole from its orientation making an angle θ 1 , with the direction of the field to θ 2 will be W = ∫ d W = ∫ θ 1 θ 2 p E sin θ d θ W = p E [ - cos θ ] θ 1 θ 2 = p E cos θ 1 - cos θ 2 This work done is stored as the potential energy u of the dipole. ∴ u = p E cos θ 1 - cos θ 2 (i) When the dipole moment p → parallel to the electric field E → θ = 0 o ), the dipole is in stable equilibrium. (ii) When the dipole moment p → is antiparallel to the electric field E → θ = 180 o ), the dipole is in unstable equilibrium.

E M B I B E

New Simplified Physics (Vol 1) For Class 12>Chapter 2 - Electrostatic Potential and Capacitance>Text Based Exercises>Q 70

EASY

12th CBSE

IMPORTANT

Earn 100

What is the electrostatic potential due to an electric dipole at an equatorial point?

Important Questions on Electrostatic Potential and Capacitance

EASY

12th CBSE

IMPORTANT

New Simplified Physics (Vol 1) For Class 12>Chapter 2 - Electrostatic Potential and Capacitance>Text Based Exercises>Q 71

A metal plate is introduced between the plates of a charged parallel plate capacitor. What is its effect on the capacitance of the capacitor?

EASY

12th CBSE

IMPORTANT

New Simplified Physics (Vol 1) For Class 12>Chapter 2 - Electrostatic Potential and Capacitance>Text Based Exercises>Q 72

A hollow metal sphere of radius

5 cm

is charged such that the potential on its surface is

10 V

. What is the potential at the centre of the sphere?

EASY

12th CBSE

IMPORTANT

New Simplified Physics (Vol 1) For Class 12>Chapter 2 - Electrostatic Potential and Capacitance>Text Based Exercises>Q 73

In which orientation, a dipole placed in the uniform electric field is in stable equilibrium?

EASY

12th CBSE

IMPORTANT

New Simplified Physics (Vol 1) For Class 12>Chapter 2 - Electrostatic Potential and Capacitance>Text Based Exercises>Q 73

In which orientation, a dipole placed in the uniform electric field is in unstable equilibrium?

EASY

12th CBSE

IMPORTANT

New Simplified Physics (Vol 1) For Class 12>Chapter 2 - Electrostatic Potential and Capacitance>Text Based Exercises>Q 74

Write the expression for the work done on an electric dipole of the dipole moment

\vec{p}

in turning, it from its position of stable equilibrium to a position of unstable equilibrium in a uniform electric field

\vec{E}

.

EASY

12th CBSE

IMPORTANT

New Simplified Physics (Vol 1) For Class 12>Chapter 2 - Electrostatic Potential and Capacitance>Text Based Exercises>Q 75

Two charges

2 μ C

and

- 2 μ C

are placed at points

A

and

B, 5 cm

apart. Depict an equipotential surface of the system.

EASY

12th CBSE

IMPORTANT

New Simplified Physics (Vol 1) For Class 12>Chapter 2 - Electrostatic Potential and Capacitance>Text Based Exercises>Q 76

What is the equivalent capacitance, $C$ , of the five capacitors, connected as shown in Figure?

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EASY

12th CBSE

IMPORTANT

New Simplified Physics (Vol 1) For Class 12>Chapter 2 - Electrostatic Potential and Capacitance>Text Based Exercises>Q 77

A charge $‘ q ’$ is moved from a point A above a dipole of dipole moment $‘ p ’$ to a point $B$ below the dipole in equatorial plane without acceleration. Find the work done in the process.

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