The magnetic field in a region is given by where L is a fixed length. A conducting rod of length L lies along the Y-axis between the origin and the point (0, L, 0). If the rod moves with a velocity v = v₀, find the emf induced between the ends of the rod.

Question

Philoid · Accepted Answer

Given:

Where B = magnetic field, y = distance from origin on y axis, L = fixed length.

Velocity of rod = v₀ i

Diagram:

Formula used:

Now, we consider a small element dy at a distance y from the origin.

Emf induced in the element dE = Bvdy, where B = magnetic field, v = velocity, dy = length of element

⇒

Integrating on both sides with proper limits, we get

=> Total emf

(Ans)

The magnetic field in a region is given by where L is a fixed length. A conducting rod of length L lies along the Y-axis between the origin and the point (0, L, 0). If the rod moves with a velocity v = v0, find the emf induced between the ends of the rod.