The net force on a current loop in a uniform magnetic field is zero, since contr

Question

The net force on a current loop in a uniform magnetic field is zero, since contributions to the net force from opposite sides of the loop cancel. However, if the field varies in magnitude from one side of the loop to the other, then a net force can be generated on the loop. Consider a square loop with sides whose length is a = 8.7 cm, located with one side at x = b = 7.4 cm in the xy plane. A magnetic field is directed along z, with a magnitude that varies with x according to
B = Bo (1 - x/d), where Bo = 0.01 T and d = 7.8 cm. If a current I = 3.3 A in the loop circulates counter-clockwise, find the magnitude |F| of the net force on the loop.
|Fnet| =

Please inlcude solution as well as answer.

Explanation / Answer

F on two horizontal segments will get cancelled out

B1 = 0.01 ( 1- 7.4/7.8) = 5.12E-4 T

B2 = 0.01 ( 1- 16.1/7.8) = - 0.0106 T

so F = I L B

F = F1 - F2 = 3.3 x 8.7E-2 x 5.12E-4 + 3.3 x 8.7E-2 x 0.0106 = 3.19E-3 N

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.