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NEET PHYSICSMOVING CHARGES AND MAGNETISMMedium

Question

A closed-loop PQRS carrying a current is placed in a uniform magnetic field. If the magnetic forces on segments PS, SR and RO (RQ) are F1F_1, F2F_2 and F3F_3 respectively and are in the plane of the paper and along with the directions shown, the force on the segment QP is

A

F3+F1−F2F_3 + F_1 - F_2

B

(F3−F1)2+F22\sqrt{(F_3 - F_1)^2 + F_2^2}

C

(F3−F1)2−F22\sqrt{(F_3 - F_1)^2 - F_2^2}

D

F3−F1+F2F_3 - F_1 + F_2

Step-by-Step Solution

  1. Net Force Principle: The net magnetic force on any closed current-carrying loop placed in a uniform magnetic field is zero. This is a fundamental result derived from the integration of the force element dF⃗=I(dl⃗×B⃗)d\vec{F} = I (d\vec{l} \times \vec{B}) over a closed loop .
  2. Vector Sum: For the loop PQRS, the vector sum of the forces on all segments must be zero: F⃗QP+F⃗PS+F⃗SR+F⃗RQ=0\vec{F}_{QP} + \vec{F}_{PS} + \vec{F}_{SR} + \vec{F}_{RQ} = 0
  3. Calculation: We need to find the force on segment QP (F⃗QP\vec{F}_{QP}). Rearranging the equilibrium equation: F⃗QP=−(F⃗PS+F⃗SR+F⃗RQ)\vec{F}_{QP} = - (\vec{F}_{PS} + \vec{F}_{SR} + \vec{F}_{RQ}) F⃗QP=−(F⃗1+F⃗2+F⃗3)\vec{F}_{QP} = - (\vec{F}_1 + \vec{F}_2 + \vec{F}_3) The magnitude of F⃗QP\vec{F}_{QP} is equal to the magnitude of the resultant of the other three forces. Based on the options provided, the expression (F3−F1)2+F22\sqrt{(F_3 - F_1)^2 + F_2^2} implies that the forces F1F_1 and F3F_3 act along the same line but in opposite directions (likely vertical components), and F2F_2 acts perpendicular to them (likely horizontal). Thus, the magnitude is the vector sum of these components: ∣F⃗QP∣=(Fvertical)2+(Fhorizontal)2=(F3−F1)2+F22|\vec{F}_{QP}| = \sqrt{(F_{vertical})^2 + (F_{horizontal})^2} = \sqrt{(F_3 - F_1)^2 + F_2^2}

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 MAGNETISMclosedloopcarryingcurrentplaceduniform

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