Question

How does the strength of the magnetic field at the center of a circular coil of wire depend on

(a). radius of the coil?

(b). number of turns of wire in the coil?

(c). strength of the current flowing in the coil?

Answer 1

Step 1: Relation between magnetic field strength and current

1. The magnetic field strength is proportional to the current flowing in the conductor.

• The relation is given by:

$\begin{array}{l}B\propto I\\ \text{where},\\ I=\text{Current flowing through wire}\end{array}$

2. The magnetic field in a straight wire carrying current can be increased by bending the conductor or wire into a circular loop.

3. The magnetic field is directly related to the number of turns in the circular loop carrying current.

• The relation is given by:

$\begin{array}{l}B\propto n\\ \text{where},\\ n=\text{Number of turns of the coil}\end{array}$

3. The magnetic field strength is indirectly proportional to the distance from the conductor carrying current.

• The relation is given by:

$\begin{array}{l}B\propto \frac{1}{r}\\ \text{where},\\ B=\text{Magnetic field strength}\\ r=\text{Radius of loop}\end{array}$

Step 2: Apply the relation

(a). When the radius of the coil is reduced, the magnetic field produced is increased as the magnetic field intensity and loop radius are inversely related.

(b). The magnetic field is directly related to the number of turns in the circular loop carrying current. So, an increase in the number of turns will also increase the magnetic field.

(c). When the magnitude of the current is increased, the magnetic field intensity is likewise increased. This is due to the fact that the magnetic field strength and current are both proportionate to each other.