Name: Electric Dipole in a Non-uniform Electric Field
Uploaded: 2019-07-19
Duration: 3 min 23 s
Description: A dipole experiences no net force in a uniform electric field. Will it exhibit similar behaviour in a non-uniform electric field? Stay tuned to find out!

Question

Obtain the formula of torque acting on an electric dipole in a uniform electric field. Two point charges of

+ 1 \times 10^{- 6}

coulomb and

- 1 \times 10^{- 6}

coulomb are situated at a distance of

2.0 cm

. The electric dipole is placed in a uniform electric field of

1 \times 10^{5} \frac{volt}{metre}

. Find the potential energy of the dipole in stable equilibrium.

Accepted Answer

Distance $= 2 cm$ . $Q = 1 \times 10^{- 6} C$ , $E = 10^{5} V / m$ ,

$∴$ Dipole moment, $P = Qd$ $= 10^{- 6} \times 2 \times 10^{- 2} = 2 \times 10^{- 8} Cm$

Torque acting on a dipole is given by, $Z = P \times E$ $= PEsinθ$

Now, Torque, $Z$ is maximum when $sinθ = 1$ , $θ = 90 °$

$∴ Z_{\max} = P \times E \times sinθ$

$= 2 \times 10^{- 8} \times 10^{5} \times 1$ $= 2 \times 10^{- 3} Nm$

Work done is given by, $W = PE [{cosθ}_{i} - {cosθ}_{F} ]$

At equilibrium $= θ_{i } = 180 °$

After rotating, $θ_{F } = 0 °$

$∴ W = - 2 PE = - 4 \times 10^{- 3} J$

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