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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 10^5nc^−1 Per Metre. - Physics

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 105NC−1 per metre. 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?

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Solution

Dipole moment of the system, p = q × dl = −10−7 C m

Rate of increase of electric field per unit length,

`"dE"/"dl"=10^-5 NC^-1`

Force (F) experienced by the system is given by the relation,

F = qE

`F=q"dE"/"dl"xxdl`

`=pxx"dE"/"dl"`

= −10−7 × 10−5

= −10−2 N

The force is −10−2 N in the negative z-direction i.e., opposite to the direction of electric field. Hence, the angle between electric field and dipole moment is 180°.

Torque (τ) is given by the relation,

τ = pE sin180°

= 0

Therefore, the torque experienced by the system is zero.

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APPEARS IN

NCERT Class 12 Physics Textbook
Chapter 1 Electric Charge and Fields
Q 27 | Page 49
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