An electric dipole of length 4 cm, when placed with its axis making an angle of 60° with a uniform electric field, experiences a torque of 4 Nm. Calculate the potential energy of the dipole, if it has charge ±8 n C.

Solution

Given,

Length of the dipole, l = 4 cm
Torque, $straight tau$ = 4 $square root of 3$ N m

Using the formula for torque, we have

Torque, τ = PEsinθ = (Ql) Esinθ ...(1)

Potential energy, U= −PEcosθ= −(Ql)Ecosθ ...(2)

Dividing equation (2) by (1),
$tau over U equals space fraction numerator left parenthesis Q l right parenthesis space E space sin space theta over denominator negative left parenthesis Q l right parenthesis space E space cos space theta end fraction space equals space minus tan space theta U space equals negative space fraction numerator tau over denominator italic tan space theta end fraction equals negative space fraction numerator tau over denominator italic tan italic 60 to the power of o end fraction$
$U equals negative fraction numerator 4 square root of 3 over denominator square root of 3 end fraction equals space minus 4 space J$

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Electrostatic Potential And Capacitance

An electric dipole of length 4 cm, when placed with its axis making an angle of 60° with a uniform electric field, experiences a torque of 4 Nm. Calculate the potential energy of the dipole, if it has charge ±8 n C.

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