Referring to the previous problem, if the dipole is allowed to rotate 90+ degree

Question

Referring to the previous problem, if the dipole is allowed to rotate 90+ degrees about it's center of mass, and Qt is fixed in position, what would be the new potential energy of Qt relative to the dipole

2. An electrie dipole with charge 50 uC and charge separation distance, d- 20 mm is centered on the origin of the x-y plane and initially aligned along the y-axis with the positive charge in the ty direction. A test charge, Q- 25 uC, is placed at x 60 mm. Calculate the total potential energy of Q relative to the dipole before any of the charges are allowed to move. 1.260 3. Referring to the previous problem, if the dipole is allowed to rotate +90 degrees about its center of mass, and Qt is fixed in position, what would be the new potential energy of Q relative to the dipole?

Explanation / Answer

3. from the given data

electric dipole charge, q = +- 50 uC

d = 20 mm

aligned along x axis

Q = 25 uC

at x = 60 mm

hence

when the +ve charge is closer to the Q

PE = kQ(q/(x - d/2) - q/(x + d/2)) = kQq(x + d/2 - x + d/2)/(x^2 - d^2/4) = 4kQq*d/(4x^2 - d^2)

PE = 64.1428 J

whenn -ve charge is closer to Q

PE = kQ(q/(x + d/2) - q/(x - d/2)) = -4kQqd/(4x^2 - d^2) = -64.1428 J

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