It is to be noted that the electric field that has been induced is (-B₁ A/2[tex]\pi[/tex]R)θ. This is obtained by using the vector units in the Cylindrical Coordinate System.
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.
The formula for Induced Electric Field is given as:
∫ E · dl = ∈
If we replace ∈ with -B₁A and 2[tex]\pi[/tex]R for dl then
∫ E · dl = -B₁A. Thus, we can state that
E∫ dl = -B₁A
Replacing or substituting 2[tex]\pi[/tex]R for ∫ dl ·E(2πR) = - B₁A
We can thus rearrange the equation to read:
E · E = ([tex]\frac{-B1A}{2\pi R}[/tex])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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