An electric dipole of length 0.5 m is placed with its axis making an angle of 30^ with uniform electric field 10^4 V/m . If it experiences a torque of 5 10⁻⁹ Nm , the magnitude of the charge on the dipole is ( 30^ = 0.5 )

Step-by-step solution

The torque experienced by an electric dipole in a uniform electric field is given by = pE where p = qd is the dipole moment, q is the magnitude of the charge, and d is the length of the dipole. Substituting p in the torque equation gives = q d E Rearranging for q yields q = d E Substituting the given values = 5 10⁻⁹ Nm , d = 0.5 10⁻⁶ m , E = 10^4 V/m , and = 30^ : q = 5 10⁻⁹ 0.5 10⁻⁶ 10^4 30^ q = 5 10⁻⁹ 0.5 10⁻² 0.5 q = 5 10⁻⁹ 0.25 10⁻² q = 20 10⁻⁷ C q = 2 10⁻⁶ C = 2 C Answer: 2 C