Question

In a region of space, a magnetic field points in the +x-direction (toward the right). Its magnitude varies with position according to the formula Bx=B0+bx, where B0 and b are positive constants, for x≥0. A flat coil of area A moves with uniform speed v from right to left with the plane of its area always perpendicular to this field. Part A What is the emf induced in this coil while it is to the right of the origin?

Answer 1

`E=Abv`

Step-by-step explanation:

We are given that

`B_x=B_0+bx`

For
`x\geq 0`

Area of coil=A

Speed=v

We have to find the emf induced in the coil while it is to the right of the origin.

We know that induced emf

`E=-(d\phi)/(dt)`

`\phi=BA`

`E=-(d(A(B_0+bx))/(dt)`

`E=-A(b)(dx)/(dt)`

We know that

`v=-(dx)/(dt)`

Substitute the value

`E=Abv`