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(i) Obtain the expression for the torque vec(tau)experiencedby an electric dipole of dipolemoment vec(p) in a uniformelectric field , vec(E ), (ii) What will happenif thefield were notuniform ? |
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Answer» Solution :(i) Takean electricdipolein an uniformfield `vec(E )`, its dipole makes angle ` theta` with electricfield(as shown)as twoforcesare equaloppositehenceconstitutetorque. Force on charge `-q` at `A = -qE` (opposite of `vec(E )`) Force of `+q` at `B = qE` (along E).  and `tau = qvecE xx AC` (Force `xx` Arm of the force) Now, `AC = AB sin theta = 2a sin theta` (`2a = " legth of dipole"`) So, `tau = qE xx 2asin theta= pEsin theta`(where `vec(p) = q xx 2a`) dipole moment. `rArr tau = vecp xx vecE`DIRECTED by RIGHT hand screw rule, here it is into the copper. (ii) If field is not uniform TEST. `F_("net") = F_(1)+F_(2) = q(E_(1) - E_(2)) = q DeltaE` for `E_(1) gt E_(2)` i.e., object (dipole) with zero CHARGEAND having net dipolemoment will experience a net force if E is non-uniform. |
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