Question

A circular loop of radius 4.0 cm is placed in a horizontal plane and carries an electric current of 5.0 A in the clockwise direction as seen from above. Find the magnetic field (a) at a point 3.0 cm above the centre of the loop (b) at a point 3.0 cm below the centre of the loop.

Answer 1

Given:
Magnitude of current, I = 5.0 A 
Radius of the loop, r = 4.0 cm 

(a) The magnetic field intensity B on point O at a distance x on the axial line is given by

\[B = \frac{\mu_0}{2}\frac{i r^2}{( x^2 + r^2 )^{3/2}}\]

\[= \frac{4\pi \times {10}^{- 7} \times 5 \times 16 \times {10}^{- 4}}{2[(9 \times 16) \times {10}^{- 4} ]^{3/2}}\]
\[ = \frac{4\pi \times 80 \times {10}^{- 11}}{2 \times 125 \times {10}^{- 6}}\]
\[ = 4 . 019 \times {10}^{- 5} T (\text{ in downward direction } )\]

(b) The magnetic field intensity B on point O' at a distance x on the axial line is given by

 

\[B = \frac{\mu_0}{2}\frac{i r^2}{( x^2 + r^2 )^{3/2}}\]

\[= \frac{4\pi \times {10}^{- 7} \times 5 \times 16 \times {10}^{- 4}}{2[(9 \times 16) \times {10}^{- 4} ]^{3/2}}\]
\[ = \frac{4\pi \times 80 \times {10}^{- 11}}{2 \times 125 \times {10}^{- 6}}\]
\[ = 4 . 019 \times {10}^{- 5} T (\text{ in downward direction } )\]