JEE Main · 2021 · 01 Sep 2021 · Shift 2 · Magnetic Effects of Current

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There are two infinitely long straight current carrying conductors and they are held at right angles to each other so that their common ends meet at the origin as shown in the figure given below. The ratio of current in both conductor is 1:1. The magnetic field at point

P

(A) $\frac{μ _{0} I}{4 π x y} [x^{2} + y^{2} - (x + y)]$
(B) $\frac{μ _{0} I}{4 π x y} [x^{2} + y^{2} + (x + y)]$ ✓ Correct
(C) $\frac{μ _{0} I x y}{4 π} [x^{2} + y^{2} - (x + y)]$
(D) $\frac{μ _{0} I x y}{4 π} [x^{2} + y^{2} + (x + y)]$

Answer: (B)

Solution

Each wire is semi-infinite, beginning at the origin. For the wire along the

x

-axis the perpendicular distance to

P

y

, and its field is

\frac{μ _{0} I}{4 π y} (1 + \frac{x}{x ^{2} + y ^{2}})

; for the wire along the

y

-axis the distance is

x

, giving

\frac{μ _{0} I}{4 π x} (1 + \frac{y}{x ^{2} + y ^{2}})

. Both fields point the same way out of the plane and add. Combining the two gives

B = \frac{μ _{0} I}{4 π x y} [x^{2} + y^{2} + (x + y)]

JEE Main · 2021 · 01 Sep 2021 · Shift 2 · Single correct option

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JEE Main · 2021 · 01 Sep 2021 · Shift 2 · Magnetic Effects of Current

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