2000 AIPMT Moving Charges and MagnetismBiot-Savart Law – Field due to Straight Wires and Arc Medium Question 5 of 5 in Biot-Savart Law – Field due to Straight Wires and Arc

For adjoining fig., the magnetic field at point 'P' will be :

For adjoining fig., the magnetic field at point 'P' will be :
A $\dfrac{\mu_0}{4\pi}$
B $\dfrac{\mu_0}{\pi}\otimes$
C $\dfrac{\mu_0}{2\pi}\otimes$
D $\dfrac{\mu_0}{2\pi}$

The answer is C.

Solution

Magnetic field of a long straight wire: $B = \dfrac{\mu_0I}{2\pi r}$
Due to the 5 A wire at 2.5 m: $B_1 = \dfrac{5\mu_0}{2\pi \times 2.5} = \dfrac{2\mu_0}{2\pi}$, directed into the page ($\otimes$) at P.
Due to the 2.5 A wire at 2.5 m: $B_2 = \dfrac{2.5\mu_0}{2\pi \times 2.5} = \dfrac{\mu_0}{2\pi}$, directed out of the page at P (opposite, since P is on the other side of this wire).
Resultant: $B = \dfrac{2\mu_0}{2\pi} - \dfrac{\mu_0}{2\pi} = \dfrac{\mu_0}{2\pi}$, into the page ($\otimes$).

Concept Superposition of fields of parallel wires

Biot-Savart Law – Field due to Straight Wires and Arc in past papers

5 questions from this chapter have appeared across 5 exam years.