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In a certain region of space, electric field is along the z-direction throughout. The magnitude of electric field is, however, not constant but increases uniformly along the positive z-direction, at the rate of 10^5 NC^(-1)per meter. What are the force and torque experienced by a system having a total dipole moment equal to 10^(-7)cm in the negative z-direction ? |
Answer» Solution : As shown in the figure, consider a point dipole (very tiny) with length dz, as shown in the figure. Its electric dipole MOMENT is, `vecp =(-vecdz)q` `therefore p = (dz)q`………..(1) Resultant electric FORCE EXERTED on above dipole by given electric field which is along + Z axis and increases with a rate `(dvecE)/(dz)`along + Z axis (as per the statement) is, `vecF = vecF_(+) + vecF_(-)` `=qvecE + (-q)(vecE + dvecE)` `=-qdvecE` `=-q (dvecE)/(dz) dz` `therefore vecF = -p (dvecE)/(dz)`............(2) (From equation (1)) Here, negative sign indicates that above force is along - Z axis. Taking magnitude, `F = p(dE)/(dz)` `=(10^(-7)) (10^(5))` `therefore F = 10^(-2) N` (Along -Z axis) Now, torque exerted on above dipole by the APPLIED electric field is, `tau = pEsin theta` `=pEsin 180^(@) (therefore vecp || -vecE)` `therefore tau =0` |
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