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

Answer:

$E=Abv$

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

$E=-\frac{d\phi}{dt}$

$\phi=BA$

$E=-\frac{d(A(B_0+bx)}{dt}$

$E=-A(b)\frac{dx}{dt}$

We know that

$v=-\frac{dx}{dt}$

Substitute the value

$E=Abv$