Question

The magnetic field at the centre of a toroid is 2.2-mT. If the toroid carries a current of 9.6 A and has 6.000 turns, what is the radius of the toroid?

Answer 1

Answer:

Radius, r = 0.00523 meters

Explanation:

It is given that,

Magnetic field, $B=2\ mT=2.2\times 10^{-3}\ T$

Current in the toroid, I = 9.6 A

Number of turns, N = 6

We need to find the radius of the toroid. The magnetic field at the center of the toroid is given by :                  

$B=\dfrac{\mu_oNI}{2\pi r}$

$r=\dfrac{\mu_oNI}{2\pi B}$  

$r=\dfrac{4\pi \times 10^{-7}\times 6\times 9.6}{2.2\pi \times 2\times 10^{-3}}$  

r = 0.00523 m

or

$r=5.23\times 10^{-3}\ m$

So, the radius of the toroid is 0.00523 meters. Hence, this is the required solution.

Answer 2

Answer:

The radius of the toroid is $5.23\times10^{-3}\ m$.

Explanation:

Given that,

Magnetic field B = 2.2 mT

Current =9.6 A

Number of turns = 6.000

We need to calculate the radius

Using formula of magnetic force

$B=\dfrac{\mu_{0}NI}{2\pi r}$

$r=\dfrac{\mu_{0}NI}{2\pi B}$

Put the value int the formula

$r=\dfrac{4\pi\times10^{-7}\times9.6\times6.000}{2\pi\times2.2\times10^{-3}}$

$r=5.23\times10^{-3}\ m$

Hence, The radius of the toroid is $5.23\times10^{-3}\ m$.