A thin metallic ring of radius 10 cm and resistance 0.01Ohm is placed in a magne

Question

A thin metallic ring of radius 10 cm and resistance 0.01Ohm is placed in a magnetic field that is changing with time as B = 10+0.1(t / sec) kˆ Gauss. The plane of the ring isperpendicular to the magnetic field.
What is the magnitude of the current inthe ring? At the center of the ring, what is the magnitude of themagnetic field generated by the induced current flowing in the ring? A thin metallic ring of radius 10 cm and resistance 0.01Ohm is placed in a magnetic field that is changing with time as B = 10+0.1(t / sec) kˆ Gauss. The plane of the ring isperpendicular to the magnetic field.
What is the magnitude of the current inthe ring? At the center of the ring, what is the magnitude of themagnetic field generated by the induced current flowing in the ring?

Explanation / Answer

   Given    Radius of the ring   r = 10cm    resistance   R = 0.01       magnitude of magneticfield   B = 10 + 0.1 t        inducesd emf         = d / dt        flux through the ring   = B A cos     here The plane of the ring isperpendicular to the magnetic field        So    = B A             = d / dt   ( B A )                     = A d B / dt                       = ( r 2 ) ( d / dt ( 10 + 0.1 t )                      =   (3.14 * 102 * 10-4 )( 0.1)                            =   3.14*10-3 V magnitude of induced current flowingin the ring   I =    3.14*10-3 V   /0.01                                                                                   =   0.314 A    magnitude of magnetic field  at thecenter of the ring                      B = o I / 2 R                        = ( 4 *10-7 )( 0.314 A )   / 2 ( 0.1)                        = 1.97 T

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