A hairpin like shape as shown in figure is made by bending a long...

A hairpin like shape as shown in figure is made by bending a long current carrying wire. What is the magnitude of a magnetic field at point $P$ which lies on the centre of the semicircle ?

A hairpin like shape as shown in figure is made by bending a long current carrying wire. What is the magnitude of a

Options

A $\dfrac{{\mu}_{0}I}{4\pir} ( 2 - \pi )$
B $\dfrac{{\mu}_{0}I}{4\pir} ( 2 + \pi )$
C $\dfrac{{\mu}_{0}I}{2\pir} ( 2 + \pi )$
D $\dfrac{{\mu}_{0}I}{2\pir} ( 2 - \pi )$

Correct answer

B. $\dfrac{{\mu}_{0}I}{4\pir} ( 2 + \pi )$

Step-by-step solution

$B = 2 \times {B}_{st . wire} + {B}_{loop}$

$B = 2 \times \dfrac{{\mu}_{0}i}{4\pir} + \dfrac{{\mu}_{0}i}{2r}\left(\dfrac{\pi}{2\pi}\right)$

$B = \dfrac{{\mu}_{0}i}{4\pir} ( 2 + \pi )$

Practice Magnetic Effects of Current on Quantrex Academy →

More from Magnetic Effects of Current

A hollow, right circular cone of base radius R and height h , with its tip at the origin… JEE Advanced 2026 In a vacuum chamber, a particle of charge 1\ and mass 1 mg is projected with a velocity (… JEE Advanced 2026 A current carrying circular loop of radius 2 cm with unit normal n = k + i 2 is placed in… JEE Main 2026 A 5 mg particle carrying a charge of 5π× 10^ -6 C is moving with velocity of (3 i +2 k )×… JEE Main 2026 A current of 30 A each flows in opposite directions in two conducting wires, placed… JEE Main 2026 A small cube of side 1 mm is placed at the centre of a circular loop of radius 10 cm… JEE Main 2026 The charged particle moving in a uniform magnetic field of (3 i + 2 j ) T has an… JEE Main 2026 A circular coil of radius 2 cm and 125 turns carries a current of 1 A. The coil is placed… JEE Main 2026 Full Magnetic Effects of Current list All JEE Main PYQs