Question:

The magnetic field at $P$ on the axis of a solenoid having $100$ turn/ $m$ and carrying a current of $5\, A$ is

Updated On: Aug 1, 2022

$250\, \mu_{0} $
$500 \,\sqrt{2} \mu_0$
$500 \,\mu_0$
$250 \,\sqrt{2} \mu_0$

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The Correct Option is D

Solution and Explanation

The magnetic field at $P$ is $B=\frac{\mu_{0} n I}{2}(\cos \theta+\cos \theta)$ where $n$ is number of turns, $I$ the current. Given, $n=100, I=5 A$ and $\theta=45^{\circ}$ $\therefore B=\frac{\mu_{0} \times 100 \times 5}{2} \times \frac{2}{\sqrt{2}}$ $\Rightarrow B =250 \sqrt{2} \,\mu_{0}$

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Concepts Used:

Magnetic Field

The magnetic field is a field created by moving electric charges. It is a force field that exerts a force on materials such as iron when they are placed in its vicinity. Magnetic fields do not require a medium to propagate; they can even propagate in a vacuum. Magnetic field also referred to as a vector field, describes the magnetic influence on moving electric charges, magnetic materials, and electric currents.

A magnetic field can be presented in two ways.

Magnetic Field Vector: The magnetic field is described mathematically as a vector field. This vector field can be plotted directly as a set of many vectors drawn on a grid. Each vector points in the direction that a compass would point and has length dependent on the strength of the magnetic force.
Magnetic Field Lines: An alternative way to represent the information contained within a vector field is with the use of field lines. Here we dispense with the grid pattern and connect the vectors with smooth lines.

Properties of Magnetic Field Lines

Magnetic field lines never cross each other
The density of the field lines indicates the strength of the field
Magnetic field lines always make closed-loops
Magnetic field lines always emerge or start from the north pole and terminate at the south pole.