Question

The diameter and number of turns of a circular coil carrying current are
respectively 31.41 x 10^-4 m and 400. Calculate the magnetic Mux density at
the center of the coil if 5 x 10^-7 A of current flows through the coil.​

Answer 1

Given :

Diameter of ring = 31.41 × 10‾⁴ m

Number of turns = 400

Current flow = 5 × 10‾⁷ A

To Find :

Intensity of magnetic field at the center of the coil.

Solution :

❖ Expression of magnetic field at the centre of a circular ring is given by

$\dag\:\underline{\boxed{\bf{\purple{B=\dfrac{\mu_oNI}{2r}}}}}$

• μ｡ denotes magnetic susceptibility
• N denotes number of turns
• I denotes current
• 2r denotes diameter

By substituting the given values;

$\sf:\implies\:B=\dfrac{\mu_oNI}{2r}$

$\sf:\implies\:B=\dfrac{(4\pi\times10^{-7})(400)(5\times 10^{-7})}{3.14\times10^{-3}}$

$\sf:\implies\:B=80\times10^{-7}\times10^2\times10^{-7}\times10^3$

$:\implies\:\underline{\boxed{\bf{\gray{B=8\times 10^{-8}\:T}}}}$

Knowledge BoosteR :

• A static charge is a source of electric field only while a moving charge is a source of both electric and magnetic fields.
• A moving charge produces a magnetic field which, in turn, exerts a force on another moving charge.
• An electric charge always experiences a force in an electric field, whether the charge is stationary or in motion.

Answer 2

Given :

Diameter of ring = 31.41 × 10‾⁴ m

Number of turns = 400

Current flow = 5 × 10‾⁷ A

To Find :

Intensity of magnetic field at the center of the coil.

Solution :

❖ Expression of magnetic field at the centre of a circular ring is given by

$\dag\:\underline{\boxed{\bf{\purple{B=\dfrac{\mu_oNI}{2r}}}}}$

μ｡ denotes magnetic susceptibility

N denotes number of turns

I denotes current

2r denotes diameter

By substituting the given values;

$\sf:\implies\:B=\dfrac{\mu_oNI}{2r}$

$\sf:\implies\:B=\dfrac{(4\pi\times10^{-7})(400)(5\times 10^{-7})}{3.14\times10^{-3}}$

$\sf:\implies\:B=80\times10^{-7}\times10^2\times10^{-7}\times10^3$

$:\implies\:\underline{\boxed{\bf{\gray{B=8\times 10^{-8}\:T}}}}$

Knowledge BoosteR :

A static charge is a source of electric field only while a moving charge is a source of both electric and magnetic fields.

A moving charge produces a magnetic field which, in turn, exerts a force on another moving charge.

An electric charge always experiences a force in an electric field, whether the charge is stationary or in motion.