Question

A loop of wire with cross-sectional area 1 m2 is inserted into a uniform magnetic field with initial strength 1 T. The field is parallel to the axis of the loop. The field begins to grow with time at a rate of 2 Teslas per hour. What is the magnitude of the induced EMF in the loop of wire

Answer 1

The magnitude of the EMF is 0.00055 volts

Step-by-step explanation:

The induced EMF is proportional to the change in magnetic flux based on Faraday's law:

`emf\,=-\,N\, (d\Phi)/(dt)`

Since in our case there is only one loop of wire, then N=1 and we get:

`emf\,=-\,N\, (d\Phi)/(dt)`

We need to express the magnetic flux given the geometry of the problem;

`\Phi=B\,\,A`where A is the area of the coil that remains unchanged with time, and B is the magnetic field that does change with time. Therefore the equation for the EMF becomes:

`emf\,=-\,N\, (d\Phi)/(dt) = (d\Phi)/(dt) =-(d\,(B\,A))/(dt) =-\,A\,(d\,(B))/(dt)=- 1\,m^2(2\,\,T/h})= -2\,\,m^2\,T/(3600\,\,s)= -0.00055\,Volts`