First slide

Electrostatic potential energy

Question

Two opposite and equal charges $4 \times 10^{- 8}$ coulomb when placed $2 \times 10^{- 2}$ cm away from a dipole. If this dipole is placed in an external electric field $4 \times 10^{8}$ newton / coulomb the value of maximum torque and the work done in rotating it through $180^{0}$ will be

Easy

A

$64 \times 10^{- 4} N m a n d 64 \times 10^{- 4} J$
B

$32 \times 10^{- 4} N m a n d 32 \times 10^{- 4} J$
C

$64 \times 10^{- 4} N m a n d 32 \times 10^{- 4} J$
D

$32 \times 10^{- 4} N m a n d 64 \times 10^{- 4} J$

Solution

Dipole moment $p = q d = 4 \times 10^{- 8} \times 2 \times 10^{- 4} = 8 \times 10^{- 12} C m$
Maximum torque $= p E \sin θ = p E \sin 90 = 8 \times 10^{- 12} \times 4 \times 10^{8} = 32 \times 10^{- 4} Nm$
Work done in rotating through $180^{0} = p E (\cos θ_{1} - \cos θ_{2}) = = p E (\cos 0 - \cos 180) = 2 p E = 2 \times 32 \times 10^{- 4} = 64 \times 10^{- 4} J$

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