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Question: In a certain region of space, electric field is along the z – direction throughout. The mangnitude o...

In a certain region of space, electric field is along the z – direction throughout. The mangnitude of electric field is however not constant, but increases uniformly along the positive z – direction at the rate of 105⥂⥂NC−1m−110^{5} ⥂ ⥂ NC^{- 1}m^{- 1}. The force experienced by the system having a total dipole moment equal to 10−710^{- 7}cm in the negative z – direction is.

A

−10−2N- 10^{- 2}N

B

10−2N10^{- 2}N

C

10−4N10^{- 4}N

D

−10−4N- 10^{- 4}N

Answer

−10−2N- 10^{- 2}N

Explanation

Solution

: Consider an electric dipole with −q- qcharge at A and +q+ q charge at B, placed along z – axis, that its dipole moment is in negative z directions.

i.e.,Pz=−107cmP_{z} = - 10^{7}cm

The electric field is along positive direction of z – axis, such that

dEdz=105NC−1m−1\frac{dE}{dz} = 10^{5}NC^{- 1}m^{- 1}

From F = qdE

=(a×dz)×dEdz= (a \times dz) \times \frac{dE}{dz}

=PdEdz= P\frac{dE}{dz}

∴F=10−7×105=−10−2N\therefore F = 10^{- 7} \times 10^{5} = - 10^{- 2}N