Question

A flat, circular loop has 15 turns. The radius of the loop is 14.5 cm and the current through the wire is 0.51 A. Determine the magnitude of the magnetic field at the center of the loop (in T).

Answer 1

`B=331.32*10^(-7)T`

Step-by-step explanation:

Given data

The current in the loop I=0.51 A

The radius of loop r=14.5m=0.145 m

Number of turns of coil n=15 turns

To find

Magnetic field B

Solution

Each segment on loop applies a magnetic field,so total magnetic field exerted by loop at any point is given by:

`B=\frac{u_(o)IR^2j}{2\pi (y^2+R^(2) )^{(3)/(2) }}`

At the center of loop y=0 so the magnitude of B of n loops of a coil

So

`B=(u_(o)nI)/(2R)`

Now plug the values to get the magnitude of B

So

`B=((4\pi *10^(-7)T.m/A)*(15)*(0.51A))/(2(0.145m)) \\B=331.32*10^(-7)T`