Question

Calculate the magnetic field induction B at the center of a circular coil having 500 turns, radius $\pi $ cm and carrying 5 A of current
a.) 0.1 T
b.) 0.005T
c.) 0.5 T
d.) 0.05 T

Answer 1

Hint: Magnetic field is a vector field which defines the region or area around which its influence can be felt. It is a type of non-contact force and does not need any type of physical contact for its action. It is the same as that of an electric field and is dependent on the distance from the source and the intensity of current in the conductor.

Complete answer:
In this question we have been asked about the strength of magnetic field due to a current carrying conductor having 500 turns
Let’s suppose that he magnetic field due to single turn is B
Magnetic field is defined as,
 ${{B}_{0}}=\dfrac{{{\mu }_{0}}I}{2r}$ ……..(1)
Where $r=\pi $ (given in the question)
I = 5A (Given in Question)
So, we can say that magnetic field due to n turns will be equal to “nB”
Where “n” is the number of turns which is equal to 500 as per our given question.
So, we can write as
$B=n{{B}_{0}}$
Now putting the value of ${{B}_{0}}$ from equation (1), we get
$B=(500)\dfrac{{{\mu }_{0}}I}{2r}$
$B=(500)\dfrac{(4\pi \times {{10}^{-}}^{7}~N{{A}^{-2}})(5)}{2\times \pi \times {{10}^{-2}}}$
$B=5\times {{10}^{-2}}T$
$B=0.05T$
Hence the value of magnetic field will be 0.05T (tesla)

We can conclude that option (d) is the correct answer for this question.

Note:
When a current passes through a conductor and magnetic field is generated and this is also the same for the current, when a conductor is placed in a magnetic field, a current is induced in it, These are defined as the law of electromagnetic induction. This law is very useful in our day-to-day life and we use electromagnets in our loudspeakers and as well as in Automatic Doors. Most of the electrical appliances that we use today work on this law of electromagnetic induction.