Question

A large solenoid of windings of \[400\] turns per meter carries a current of \[5\,{\text{A}}\]. The magnetic field at the centre of the solenoid is about:
A. \[1.2\,{\text{mT}}\,\]
B. Zero
C. \[5.0\,{\text{mT}}\,\]
D. \[2.5\,{\text{mT}}\,\]

Answer 1

Hint: First of all, we will find a formula which states that magnetic field is directly proportional to number of turns and current flowing through. WE will substitute the required values and manipulate accordingly to obtain the result.

Complete step by step answer:
In the given question, we are supplied with the following data:
The number of turns that the solenoid has is \[400\] turns per meter.
The amount of current flowing through the coil is \[5\,{\text{A}}\] .
We are asked to find the magnetic field at the centre of the solenoid.

To begin with, we have the number of turns and current flowing already supplied with the question.
So, we will use the formula which is given below:
\[B = \mu \times n \times I\] …… (1)
Where,
\[B\] indicates the magnetic field.
\[\mu \] indicates permeability constant.
\[n\] indicates the number of turns.
\[I\] indicates current flowing through the coil of the solenoid.

Now, we substitute the required values in the equation (1), we get:
$B = \mu \times n \times I \\$
$\implies B = 4\pi \times {10^{ - 7}} \times 400 \times 5 \\$
$\implies B = 2.512 \times {10^{ - 3}}\,{\text{T}} \\$
$\therefore B = 2.512\,{\text{mT}} \\$
It can be rewritten as:
\[B \sim 2.5\,{\text{mT}}\]
Hence, the magnetic field at the centre of the solenoid is about \[2.5\,{\text{mT}}\] .

So, the correct answer is “Option D”.

Additional Information:
A solenoid is a type of electromagnet whose function is to produce a regulated magnetic field into a closely packed helix via a coil wound. The coil can be arranged as an electrical current is passing through it to create a uniform magnetic field in a volume of space.

Note:
The given problem is based on the magnetic field due to solenoid. Higher the value of the magnetic field is, higher is the strength of the field. The strength of the magnetic field increases on increasing the number of turns per unit length or the magnitude of current.