Question

A flat circular coil with 167 turns, a radius of 5.73 x 10-2 m, and a resistance of 0.228 2 is exposed to an external magnetic field that is directed perpendicular to the plane of the coil. The magnitude of the external magnetic field is changing at a rate of AB/At = 0.628 T/s, thereby inducing a current in the coil. Find the magnitude of the magnetic field at the center of the coil that is produced by the induced current. Number Units

Answer 1

- Son : sol. According to Faraday's law, the induced emf in the coil is given by - e= - 49 ; where he is the change in ao flux associated with the coil Again, the flux associated with the coil is 1 p = BNA ; where N is the no. of twins, A is the area of coil and B is the external magnetic field. ie= -'4(BNA) & NA Tas n and A fixed ] Now, A=TR? [R = radius of cail] = 7x (5.73 x 10-2)2 = 0.0103 m² = 1.03810-2 m2 Given, N= A HE 167 tuins = 0.628 T/S .. e = - 0.628 x 167 X 1.03 x10-2 CS Scanned with = -1:08 V CamScanner

- Thus the magnitude of the induced emf in the coil, lel = 1.08 V so the current flowing through the coil. I= emf in the coil resistance of the coll = 1.08 0.228 = 4.74 A. so the magnetic field at the centre of the coil due to this induced emf or induced current, Bare NETB) = MONI R² R => B = (471 X10-7) x 167 x 4.74 2x (5073 X10-2) = 8.68 X10-3 of Scanned with CamScanner