Question

A circular coil of wire consisting of 100turns each of radius 9cm carries 0.4A. The magnitude of the magnetic field at the center of the coil is:
A) $2.4 \times {10^{ - 4}}T$
B) $3.5 \times {10^{ - 4}}T$
C) $2.97 \times {10^{ - 4}}T$
D) $3 \times {10^{ - 4}}T$

Answer 1

Hint: The magnetic field around the center of the circular coil can directly depend on the number of coils, the permittivity of free space, and current flows through the coil. The current flowing through the coil increases as the number of turns decreases.

Formula used :
The expression for finding the magnetic field at the center of a circular coil of N turns is given by the following formula.
$B = \dfrac{{{\mu _0}IN}}{{2r}}$
Where $r$ is the radius, $N$ is the number of turns, and ${\mu _0}$ is the permittivity of free space.

Complete step by step answer:
Given, The number of turn is ${\text{N = 100}}$
The current is $I = 0.4\;{\text{A}}$
The radius of the coil is $r = 9\;{\text{cm = 0}}{\text{.09}}\;{\text{m}}$
Let us now use the formula of magnetic field at the center of circular coil $B = \dfrac{{{\mu _0}IN}}{{2r}}$
Let us substitute the values.
$B = \dfrac{{4\pi \times {{10}^{ - 7}} \times 0.4 \times 100}}{{2 \times 0.09}}$
Let us simplify the expression.
$B = 2791.11 \times {10^{ - 7}} = 2.79 \times {10^{ - 4}}T$

$\therefore $ We can say that option (C) is correct.

Additional information:
- The magnetic field is the area around a magnet in which there is a magnetic force and also Moving charges can make magnetic fields.
- fields can be shown by magnetic flux lines. The direction of the magnetic flux lines in the direction of the magnetic field.
- The strength of a magnet is defined by the spaces between the magnetic flux lines. If the flux lines are closer to each other, the stronger the magnet is. The farther away they are, the weaker.
- To see the flux lines we can place iron filings over a magnet. The iron filings move and arrange into the flux lines. Hence, we can say that Magnetic fields give power to other particles that touch the magnetic field.

Note:
The electric current in a circular coil creates a magnetic field that is more concentrated in the center of the coil than outside of the coil. The permittivity of free space value should remember to calculate the magnetic field around the coil. When the radius increases the center of the magnetic field around the coil decreases.