Question

Consider a conductor carrying current ‘I’, P is a point at a distance away from the conductor.

1. What is the direction of magnetic field at P?

2. What are the factors affecting magnetic field at P due the element dl carrying current i? 

3. Derive an expression for magnetic field at P, if the current carrying conductor has infinite length?

4. Draw a graph connecting Intensity of magnetic field and distance. 

Answer 1

1. In to the plane of paper

2. dB = \(\frac{\mu_0}{4\pi}\frac{|d|sinθ}{r^2}\)

• Current I
• Length of element dl
• sin of angle between element and line joining mid point of element and point.
• Inversely proportional to square of the distance between element and point.

3. Long straight conductor:

Consider a long straight conductor carrying ‘I’ ampere current. To find magnetic field at ‘P’, we construct a circle of radius r (passing through P).

According to Ampere’s circuital law we can write

4.