Points to correct step by step solutions and explanations A wire is bent so that
ID: 2257858 • Letter: P
Question
Points to correct step by step solutions and explanations
A wire is bent so that it forms the arc of two partial circles complete except for an angle alpha, and these partial circles are connected by two radial pieces, all as shown. The inner partial circle has a radius R 1, and the outer partial circle has a radius R 2 The center of the circles is the point C. A current, I, goes through the wire as shown Use the Biot-Savart law to find the magnetic field at the point C due to current in both straight radial wires, Use the Biot-Savart law to find the magnetic field at the point C due to current in the inner partial circle of wire, Use the Biot-Savart law to find the magnetic field at the point C due to current in the outer partial circle of wire,Explanation / Answer
The straight lines can be extended to reach the origin, thus the field B due to them will be 0.
Magnetic field due to the whole circular circle will be ki / 2r ..............where k is the permeability of vaccuum.
But, in the question, only 2(pi) - (alpha) degrees is subtended by the coil.
Thus magnetic field B = ki / 2r * [2(pi) - (alpha)] / 2(pi)
In the first case , due to the inner wire, we will put r = R1 ; and since direction of current is clockwise
the field is inward.
In the second, due to the outer wire r = R2, and since direction is anti-clockwise,
the field is outward.
The total magnetic field would be
= 1/2 * ki [ 2(pi) - (alpha)] * [ (1/R1) - (1/R2) ]
this would be going into the plane.
THANK YOU. DO RATE