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(B) The torque $	au$ acting on an electric dipole in a uniform electric field $E$ is given by the formula: $	au = pE \sin 	heta$. Given: $	au = 20

Vedclass · Accepted Answer

$-60$

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(B) The torque $	au$ acting on an electric dipole in a uniform electric field $E$ is given by the formula: $	au = pE \sin 	heta$. Given: $	au = 20 \sqrt{3} \ Nm$,$	heta = 30^{\circ}$,and $E = 10^6 \ N/C$. Substituting the values: $20 \sqrt{3} = pE \sin 30^{\circ} = pE 	imes (1/2)$. Therefore,$pE = 40 \sqrt{3} \ Nm$. The potential energy $U$ of an electric dipole in an external electric field is given by: $U = -pE \cos 	heta$. Substituting the values: $U = -(40 \sqrt{3}) \cos 30^{\circ} = -(40 \sqrt{3}) 	imes (\sqrt{3}/2)$. $U = -40 	imes (3/2) = -60 \ J$.

An electric dipole of length $4 \ cm$ is placed with its axis making an angle of $30^{\circ}$ with a uniform electric field of $10^6 \ N/C$. If it experiences a torque of $20 \sqrt{3} \ Nm$,then the potential energy of the dipole is $:-$ (in $J$)

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