Magnetism-

 

Before you go through this article, make sure that you have gone through the previous article on Magnetic Field Due To Circular Current Carrying Loop.

 

We have learnt-

• A current carrying conductor produces a magnetic field around it.
• The magnetic field at the center of a current carrying loop is given by the formula-

 

 

In this article, we will learn about the magnetic field at the center of a circular current carrying arc.

 

Magnetic Field At The Center of Circular Current Carrying Arc-

 

Consider a circular arc of wire of radius R carrying current I and subtending an angle θ at its center. We wish to determine the magnetic field at its center.

 

The arc can be assumed to be made up of a large number of small current elements. We consider one such current element of the loop as shown-

 

 

Using Biot-Savart law, the magnitude of the magnetic field dB at the center O due to this current element is given by-

 

 

The net magnetic field due to all such current elements of the arc at center O is given by-

 

 

Thus, the net magnetic field at the center of a circular current carrying arc is given by-

 

 

This formula is used to calculate the magnitude of the magnetic field due to a circular current carrying arc subtending an angle θ at its center.

 

Important Note While using the above formula, the value of θ must be put in radians.

 

It is interesting to note the magnetic field at the center of the current carrying arc in terms of the magnetic field at the center of current carrying loop.

 

Let the magnetic field at the center of complete current carrying loop is B_o. Then, for a circular current carrying arc having the same radius, we have-

 

Angle Subtended At Center of Arc	Magnetic Field At Center of Arc (in terms of Bo)
360°	Bo
180°	Bo / 2
120°	Bo / 3
90°	Bo / 4
60°	Bo / 6
30°	Bo / 12

 

MCQs Quiz-

MCQs Quiz

on Magnetic Field At Center of Circular Current Arc

 

Worksheet-

Worksheet

on Magnetic Field At Center of Circular Current Arc

 

Next Article-

Magnetic Field On Axis of Circular Current Carrying Loop

 

Get more notes & other study material of the Chapter Moving Charges & Magnetism.