A magnetic field that is uniform in space, but whose magnitude changes with time at a constant rate, is directed along the x-axis. A conducting ring of diameter 7.0 cm and electrical resistance 1.5x10-3 Ω lies in the y-z plane. If the induced current in the ring is observed to be 2.0 A, what is the rate of change (in T/s) of the magnitude of the magnetic field?

Respuesta :

Answer:

0.24T/s

Explanation:

This problem can be solved if use the Lenz's Law, that is

[tex]\epsilon=-\frac{d\Phi_{B}}{dt}=-\frac{d(B*S)}{dt}[/tex]        ( 1 )

but this emf is for the ring:

[tex]\epsilon=IR\\\epsilon=(2.0A)(1.5*10^{-3})=3.75*10^{-3}V[/tex]

and we can replace this value in ( 1 )

[tex]3.75*10^{-3}V=-S\frac{dB}{dt}=-\pi (0.07m)^{2}\frac{dB}{dt}\\\frac{dB}{dt}=\frac{3.75*10^{-3}V}{\pi (0.07m)^{2}}=0.24\frac{T}{s}[/tex]

where we have taken the area of a circle and a radius of 70cm=0.07m. dB/dt is the ratio of change of the magnetic field. Hence the answer is 0.24T/s

I hope this is useful for you

regards