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Class 12 › Physics › Moving Charges and Magnetism
CBSE2021Class Class 12 · Physics3 Marks · Short✅ Verified
A straight wire carrying 12 A is bent into a semicircular arc of radius 2 cm.
(a) Find the direction and magnitude of magnetic field at the centre of the arc.
(b) Would your answer change if the wire were bent in the opposite way?
✅ Answer & Solution
(a) Magnetic field due to semicircular arc at centre:
$$B = \frac{\mu_0 I}{4R} = \frac{4\pi \times 10^{-7} \times 12}{4 \times 0.02}$$
$$B = \frac{4\pi \times 10^{-7} \times 12}{0.08} = 6\pi \times 10^{-5} \approx 1.885 \times 10^{-4} \text{ T}$$
Direction: into the page (by right-hand rule, for current flowing as shown).
(b) If bent in opposite direction:
The magnitude remains the same ($B = 1.885 \times 10^{-4}$ T) but the direction reverses — out of the page.
The straight portions of wire on both sides pass through the centre, so they contribute zero field.
