Question

A current of 10A is passing through a long wire which has semicircular loop of the radius 20cm as shown in figure . Magnetic field produced at the centre of the loop is ??

Answer 1

Answer:

The magnetic field produced at the center of the loop is $B=5 \pi \mu \mathbf{T}$

Explanation:

Step 1: The Biot-Savart law is an equation that describes the magnetic field produced by a constant electric current in physics, especially electromagnetism. It connects the electric current's strength, direction, length, and closeness to the magnetic field.

Given:

Current passing through the loop $I=10 \mathrm{~A}$

Radius of the loop$R=20 \times 10^{-2} \mathrm{~m}$

From the biot-savert law, magnetic field in current carrying loop is given by,

$B=\frac{\mu_0 I}{2 R}$

Where$\mu_o=4 \pi \times 10^{-7}$

Step 2:The magnetic impact on moving electric charges, electric currents, and magnetic materials is described by a magnetic field, which is a vector field. A force perpendicular to the charge's own velocity and the magnetic field acts on it while the charge is travelling through a magnetic field.

In our example loop is half so our above equation is modified as follows,

$\begin{aligned}& B=\frac{\mu_a I}{4 R} \\& B=\frac{4 \pi \times 10^{-7} \times 10}{4 \times 20 \times 10^{-2}} \\& B=5 \pi \mu\end{aligned}$

Step 3: Hence, The magnetic field produced at the center of the loop is $B=5 \pi \mu \mathbf{T}$.

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