Question

A solenoid $2.5{\rm{ m}}$ length and $2.0{\rm{ cm}}$ diameter possesses $10$ turns per cm.
A current of $0.5{\rm{ A}}$is flowing through it. The magnetic induction at axis inside the
solenoid is then,
A. $2\pi \times {10^{ - 4}}T$
B. $2\pi \times {10^{ - 5}}T$
C. $2\pi \times {10^{ - 6}}T$
D. $2\pi \times {10^{ - 7}}T$

Answer 1

Solution:
Hint: A solenoid is a long coil of wire wrapped in many turns in a cylinder. When a current pass
through it, it creates a nearly uniform magnetic field inside. The direction of magnetic field
depends on the direction of the current flowing. The magnetic induction at axis inside the
solenoid is calculated using the formula, $B = {\mu _0}NI{\rm{ Tesla}}$, where B is the
magnetic field density, ${\mu _0}$is the permeability of free space, $N$ is the number of turns
and $I$is the current flowing through the coil. The magnetic field generated along the axis of a solenoid is proportional to the number of turns per unit length and the current flowing in it.
Complete step by step solution:
Given,
Length of the solenoid, $l = 2.5{\rm{ m}}$
Diameter of the solenoid, $d = 2.0{\rm{ cm}}$
Number of turns per cm, $n = 10{\rm{ turns per cm = 1000 turns per m}}$
The formula for magnetic field at axis inside the solenoid is given as,
$B = {\mu _0}NI{\rm{ Tesla}}$ …….(1)
This formula is also known as Ampere’s Law.
Substituting, $4\pi \times {10^{ - 7}}$ in ${\mu _0}$, $1000$ in $N$ and $0.5{\rm{ A}}$ in $I$
in equation (1) we get,
$B = 4\pi \times {10^{ - 7}} \times 1000 \times 0.5 = 2\pi \times {10^{ - 4}}T$
Hence, the correct answer is (A).
Note: the students have to apply the concept of magnetic field production when a current flow
through a current carrying conductor or coil. The direction of magnetic field depends on the
direction of current and the value of magnetic field can be calculated from the number of turns in
the coil, the permeability of free space and the amount of current flowing through the coil. A
Solenoid is used as an electromagnet which can provide a simple and strong magnetic field. It is
mainly used to convert electrical motion to mechanical motion like in plungers.