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  • (a) Show that a current carrying solenoid behaves like a small bar magnet. Obtain the expression for the magnetic field at an external point lying on its axis. (b) A steady current of 2A flows through a circular coil having 5 turns of radius

(a) Show that a current carrying solenoid behaves like a small bar magnet. Obtain the expression for the magnetic field at an external point lying on its axis.

(b) A steady current of 2A flows through a circular coil having 5 turns of radius 7 cm. The coil lies in X-Y plane with its centre at the origin. Find the magnitude and direction of the magnetic dipole moment of the coil.

 

 
 
 
 
 

Answers (1)

(a) A solenoid may be regarded as a combination of a large number of identical circular current loops in which each behaves like a magnetic dipole. Hence, the current-carrying
the solenoid will behave like a small bar magnet.

 

The magnetic field at P due to small element dx is 

dB = \frac{\mu _{0}ndxIa^{2}}{2\left [ \left ( r-x \right )^{2}+a^{2} \right ]^{\frac{3}{2}}}

for r>>>a and r>>> x

B\approx \frac{\mu _{0}nIa^{2}}{2r^{3}}\int_{-l}^{l}dx

dB= \frac{\mu _{0}nIa^{2}2l}{2r^{3}}

Magnetic moment

 m = n2l(\pi a^{2})

\therefore B = \frac{\mu_{0}2m}{4\pi r^{3}}

b) 

M=NI\times \pi a^2

=5\times2\times \pi\times49\times10^{-4}=0.154Am^2

M will be parallel to Z axis

Posted by

Safeer PP

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