JEE Main · 2024 · 31 Jan 2024 · Shift 1 · Magnetic Effects of Current

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A rigid wire consists of a semicircular portion of radius R and two straight sections. The wire is partially immerged in a perpendicular magnetic field

B = B_{0} \hat{j}

as shown in figure. The magnetic force on the wire if it has a current

i

is :

(A) $- iBR \hat{j}$
(B) $2 iBR \hat{j}$
(C) $i B R \hat{j}$
(D) $- 2 iBR \hat{j}$ ✓ Correct

Answer: (D)

Solution

For a current-carrying wire of any shape in a uniform magnetic field, the net magnetic force depends only on the straight-line vector joining its two ends:

F = i L \times B

For the semicircular portion of radius

R

(with the straight sections lying along the line joining its two ends), the end-to-end separation is the diameter,

2 R

. With

B = B_{0} \hat{j}

and the current direction and orientation shown in the figure, this gives

F = - 2 i B_{0} R \hat{j}

JEE Main · 2024 · 31 Jan 2024 · Shift 1 · Single correct option

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JEE Main · 2024 · 31 Jan 2024 · Shift 1 · Magnetic Effects of Current

Solution

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