Chapter 28, Problem 052 In the figure, a rectangular loop carrying current lies

Question

Chapter 28, Problem 052 In the figure, a rectangular loop carrying current lies in the plane of a uniform magnetic field of magnitude 0.0589 T. The loop consists of a single turn of flexible conducting wire that is wrapped around a flexible mount such that the dimensions of the rectangle can be changed. (The total length of the wire is not changed.) As edge length x Is varled from approximately zero to Its maxlmum value of approximately 4.24 cm, the magnitude T of the torque on the loop changes. The maximum value of T is 3.34 x 108 N*m. What is the current in the loop? Number Units the tolerance is +/-5%

Explanation / Answer

052. given B = 0.0589 T
now, Torque T = BiA
for Maximum torque
3.34*10^-8 = 0.0589*i*A

now, for a rectangle of perimenter l
area A = (l - 2x)/2 * x = (lx/2 - x^2)
for maximum area
dA/dx = 0
l/2 = 2x
hence
l = x/4
hence A = x^2
hence
i = 0.3154274 mA

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