A dipole of moment 0.50 e nm is placed in a uniform electric field with a magnit

Question

A dipole of moment 0.50 e nm is placed in a uniform electric field with a magnitude of 4.0% 104 N/C. what is the magnitude of the torque on the dipole for each of the following situations? (a) the dipole is aligned with the electric field N·m (b) the dipole is transverse to (perpendicular to) the electric field N·m (c) the dipole makes an angle of 25° with the direction of the electric field N·m (d) Defining the potential energy to be zero when the dipole is transverse to the electric field, find the potential energy of the dipole in the electric field for the orientations specified in Parts (a) and (c) =0°, U = eBook

Explanation / Answer

p = 0.50 e - nm = (0.50)(1.6 x 10^-19)(10^-9)

p = 8 x 10^-29 C m

E = 4 x 10^4 N/C

(A) torque = p x E = p E sin(theta)

when p and E are aligned then theta = 0

sin(0) = 0

torque = 0

(B) now theta = 90 deg

torque = (8 x 10^-29)(4 x 10^4) sin90

= 3.2 x 10^-24 N m

(C) torque = p E sin25

= 1.35 x 10^-24 N m

(D) U = - p.E = - p E cos(theta)

theta = 0 , U = - p E cos0 = - 3.2 x 10^-24 J

tehta = 25 deg, U = - P E cos25 = - 1.35 x 10^-24 J

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