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NEET PHYSICSMOVING CHARGES AND MAGNETISMHard

Question

Two identical long conducting wires AOBAOB and CODCOD are placed at right angle to each other, with one above other such that OO is their common point for the two. The wires carry I1I_1 and I2I_2 currents, respectively. Point PP is lying at distance dd from OO along a direction perpendicular to the plane containing the wires. The magnetic field at the point PP will be:

A

μ02πd(I1I2)\frac{\mu_0}{2\pi d} (\frac{I_1}{I_2})

B

μ02πd(I1+I2)\frac{\mu_0}{2\pi d} (I_1 + I_2)

C

μ02πd(I12−I22)\frac{\mu_0}{2\pi d} (I_1^2 - I_2^2)

D

μ02πd(I12+I22)1/2\frac{\mu_0}{2\pi d} (I_1^2 + I_2^2)^{1/2}

Step-by-Step Solution

According to the sources, the magnetic field BB produced by a long straight wire carrying current II at a distance dd is given by B=μ0I2πdB = \frac{\mu_0 I}{2\pi d} .

  1. Field from Wire 1 (B1B_1): For the wire carrying current I1I_1, the magnetic field at point PP (at a perpendicular distance dd) is B1=μ0I12πdB_1 = \frac{\mu_0 I_1}{2\pi d}. Using the right-hand rule, this field vector lies in the plane of the wires, perpendicular to the first wire.
  2. Field from Wire 2 (B2B_2): Similarly, for the wire carrying current I2I_2, the magnetic field at point PP is B2=μ0I22πdB_2 = \frac{\mu_0 I_2}{2\pi d}. This field vector also lies in the plane of the wires but is perpendicular to the second wire.
  3. Resultant Field (BB): Since the two wires are at right angles, the magnetic field vectors B⃗1\vec{B}_1 and B⃗2\vec{B}_2 they produce at point PP are also perpendicular to each other. The magnitude of the net magnetic field is calculated using the Pythagorean theorem: B=B12+B22B = \sqrt{B_1^2 + B_2^2}.

Substituting the values: B=(μ0I12πd)2+(μ0I22πd)2=μ02πdI12+I22B = \sqrt{(\frac{\mu_0 I_1}{2\pi d})^2 + (\frac{\mu_0 I_2}{2\pi d})^2} = \frac{\mu_0}{2\pi d} \sqrt{I_1^2 + I_2^2}, which can be written as μ02πd(I12+I22)1/2\frac{\mu_0}{2\pi d} (I_1^2 + I_2^2)^{1/2}.

Exam Context & Concepts Covered

This question aligns with the NEET PHYSICS syllabus, specifically targeting concepts from MOVING CHARGES AND MAGNETISM. Mastering this topic is crucial for scoring well in the upcoming medical entrance examinations. Solving conceptually related problems will help you understand the nuances of these concepts and improve your problem-solving speed.

PHYSICSMOVING CHARGES AND MAGNETISMidenticalconductingplacedcommoncurrents

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