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Ampere's Circuital Law

A solenoid of...

Question

A solenoid of length $l$ and having $n$ turns carries a current $i$ in anticlockwise direction. The magnetic field produced by it is :

A

μ_{0} n i

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B

μ_{0} n i / l

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C

Along the axis of solenoid

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D

Perpendicular to the axis of coil

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Solution

The correct options are
B Perpendicular to the axis of coil
C Along the axis of solenoid
D $μ_{0} n i / l$
A solenoid of length $l$ and having $n$ turns carries a current i in anticlockwise direction.
The magnetic field is $\frac{μ_{0} n i}{l}$ . Its directions will be along the axis of solenoid and perpendicular to the axis of coil.

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Q. A tightly-wound solenoid of radius a and length l has n turns per unit length. It carries an electric current i. Consider a length dx of the solenoid at a distance x from one end. This contains n dx turns and may be approximated as a circular current i n dx. (a) Write the magnetic field at the centre of the solenoid due to this circular current. Integrate this expression under proper limits to find the magnetic field at the centre of the solenoid. (b) verify that if l >> a, the field tends to B = µ₀ni and if a >> l, the field tends to

B = \frac{μ_{0} n i l}{2 a}

. Interpret these results.

Q. A tightly-wound, long solenoid is kept with its axis parallel to a large metal sheet carrying a surface current. The surface current through a width dl of the sheet is Kdl and the number of turns per unit length of the solenoid is n. The magnetic field near the centre of the solenoid is found to be zero. (a) Find the current in the solenoid. (b) If the solenoid is rotated to make its axis perpendicular to the metal sheet, what would be the magnitude of the magnetic field near its centre?

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