Question

Due to the cylindrical symmetry of this problem, the induced electric field E⃗ (R,t) can depend only on the distance R from the z axis, where R is restricted to the region outside the iron rod. Find this field. Express E⃗ (R,t) in terms of quantities given in the introduction (and constants), using the unit vectors in the cylindrical coordinate system, θ^, r^, and k^

Answer 1

It is to be noted that the electric field that has been induced is (-B₁ A/2$\pi$R)θ. This is obtained by using the vector units in the Cylindrical Coordinate System.

What are Cylindrical Coordinates?

Cylindrical Coordinates are simply defined as a component of a coordinate system that is used to locate a location in space using its polar coordinates and vertical distance from the polar plane.

How is the induced field arrived at?

The formula for Induced Electric Field is given as:

∫ E · dl = ∈

If we replace ∈ with -B₁A and 2$\pi$R for dl then

∫ E · dl = -B₁A. Thus, we can state that

E∫ dl  = -B₁A

Replacing or substituting 2$\pi$R for ∫ dl ·E(2πR)  = - B₁A

We can thus rearrange the equation to read:

E · E = ($\frac{-B1A}{2\pi R}$)θ

It is to be noted that the circumference of a circle is the integral of the length of the element. While θ, which in this case is the unit vector refers to the Cylindrical Coordinate and the direction of the electric field.

Learn more about Cylindrical Coordinates at:

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