Question

Magnetic field at the centre of a coil in the form of a square of side 4 cm carrying a current of 5 A is

Answer 1

Answer:

A coil in the form of a square of side 2acarries a curent I.

Consider wire AB. 

distance from C=a [Ref. image 1]

Now, magnetic field due to a finite wire carrying current I at a point is given by (at a distance r)

B=2πrμ0I(sin∝+sinB) [Ref. image 2]

So magnetic field at B due to AB:-

B1=4πaμ0I(sin45o+sin45o)

B1=4πaμ0I(2)       [From geometry, ∝=β=45o]

Similarly, other wires contribute to same field in same direction given as:-

B=4B1=4×4πaμoI(2)

⇒B=2πaμ0I