The figure below shows a wire ring of radius a = 1.8 cm that is perpendicular to
ID: 2269572 • Letter: T
Question
The figure below shows a wire ring of radius a = 1.8 cm that is perpendicular to the general direction of a radially symmetric, diverging magnetic field. The magnetic field at the ring is everywhere of the same magnitude B = 3.4 mT, and its direction at the ring everywhere makes an angle ? = 20
The figure below shows a wire ring of radius a = 1.8 cm that is perpendicular to the general direction of a radially symmetric, diverging magnetic field. The magnetic field at the ring is everywhere of the same magnitude B = 3.4 mT, and its direction at the ring everywhere makes an angle ? = 20degree with a normal to the plane of the ring. The twisted lead wires have no effect on the problem. Find the magnitude of the force the field exerts on the ring if the ring carries a current i = 5.4 mA.Explanation / Answer
On any differential length dL of the ring, dF = idL x B. By the RHR, this is directed inward at an angle of q above the horizontal. By symmetry, the radial component cancels out on integration around the loop, but the vertical component is in the upward direction and has the same magnitude for each part of the differential path ds. Thus, F = iLB = 2?iaB sin(q) = 2?(5,4 x 10-3 A)(0.018 m)(3.4 x 10-3 T) sin(20O) = 0.20
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