Question

How r cube change into r square in biotsavartlaw

Answer 1

In the biot-savart law B = i (dl x r) /r³ * μ/4π

We are getting the vector product of dl and r vector

but in other for ie B = i (dl x 1r) /r² * μ/4π here 1r is unit vector in the direction of r vector.

In the first case we multiply the direction as well as magnitude of r vector so we need to divide it by another r so it is r³ in denominator but in the second case we are only multiplying direction so we need not divide magnitude again. So we get r² in denominator.

I hope you understand.