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 - Physics

Numerical

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 105 NC−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?

Solution

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

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" xx "dl"

= "p" xx "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 the electric field. Hence, the angle between the electric field and the dipole moment is 180°.

Torque (τ) is given by the relation,

τ = pE sin 180°

= 0

Therefore, the torque experienced by the system is zero.

Concept: Dipole in a Uniform External Field
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APPEARS IN

NCERT Physics Part 1 and 2 Class 12
Chapter 1 Electric Charges and Fields
Exercise | Q 1.27 | Page 49
NCERT Class 12 Physics Textbook
Chapter 1 Electric Charge and Fields
Exercise | Q 27 | Page 49
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