Question

Suppose I have a circular loop of wire with radius R. I run a current I through the loop and measure a magnetic field B at the center of the wire. If I double the radius of the wire and triple the current in the wire, what is the new magnetic field at the center of the wire

Answer 1

Explanation:

The magnetic field at the center of the wire is given by :

$B=\dfrac{\mu_oI}{2r}$

Here,

I is current flowing throgh the loop

r is the radius of loop

If the radius of the wire is doubled and the current is tripled, then new magnetic field is given by :

$B'=\dfrac{\mu_oI'}{2r'}\\\\B'=\dfrac{\mu_o(3I)}{2(2r)}\\\\B'=\dfrac{3}{2}\times \dfrac{\mu_oI}{2r}\\\\B'=\dfrac{3}{2}\times B$

So, the new value of magnetic field gets 3/2th of the initial magnetic field.