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Concepts Of Physics MCQ Edition [Volume 2]
Exam
Concepts Of Physics MCQ Edition [Volume 2]
Subject
Physics
Chapter
Magnetic Field

Concepts Of Physics MCQ Edition [Volume 2] · Physics · Magnetic Field

A 2 A current enters at the corner d of a square frame abcd having...

A 2 A2 \text{ A} current enters at the corner dd of a square frame abcdabcd having a side length of 20 cm20 \text{ cm} and exits at the opposite corner bb. A magnetic field B=0.1 TB = 0.1 \text{ T} is present in the region, directed perpendicular to the plane of the frame as shown in the figure. Determine the magnitude and direction of the magnetic forces acting on the four sides of the frame.
A 2 A current enters at the corner d of a square frame abcd having a side length of 20 cm and exits at the opposite

Options

  1. A0.04 N0.04 \text{ N} on each wire; on dada and cbcb towards right, and on dcdc and abab upward
  2. B0.02 N0.02 \text{ N} on each wire; on dada and cbcb towards left, and on dcdc and abab downward
  3. C0.04 N0.04 \text{ N} on each wire; on dada and cbcb towards left, and on dcdc and abab downward
  4. D0.02 N0.02 \text{ N} on each wire; on dada and cbcb towards right, and on dcdc and abab upward

Correct answer

B. 0.02 N0.02 \text{ N} on each wire; on dada and cbcb towards left, and on dcdc and abab downward

Step-by-step solution

The total current entering the square frame at corner dd is I=2 AI = 2 \text{ A}.

Since the frame is a square made of uniform wire, the resistance of the path d→a→bd \to a \to b is equal to the resistance of the path d→c→bd \to c \to b. Therefore, the current splits equally into the two branches.

Current in each side of the frame is:
Ida=Iab=Idc=Icb=22=1 AI_{da} = I_{ab} = I_{dc} = I_{cb} = \dfrac{2}{2} = 1 \text{ A}

The magnetic field is uniform, directed perpendicular to the plane of the frame and outwards (indicated by dots), so B⃗=0.1k^ T\vec{B} = 0.1 \hat{k} \text{ T}.

The magnitude of the magnetic force on each wire of length L=20 cm=0.2 mL = 20 \text{ cm} = 0.2 \text{ m} is given by:
F=ILBsin⁡(90∘)=1×0.2×0.1=0.02 NF = I L B \sin(90^{\circ}) = 1 \times 0.2 \times 0.1 = 0.02 \text{ N}

The direction of the force on each wire can be found using F⃗=I(L⃗×B⃗)\vec{F} = I(\vec{L} \times \vec{B}):
For wire dada: Current is downwards (−j^-\hat{j}). F⃗da=1(−0.2j^×0.1k^)=−0.02i^ N\vec{F}_{da} = 1(-0.2\hat{j} \times 0.1\hat{k}) = -0.02\hat{i} \text{ N} (towards left).
For wire cbcb: Current is downwards (−j^-\hat{j}). F⃗cb=1(−0.2j^×0.1k^)=−0.02i^ N\vec{F}_{cb} = 1(-0.2\hat{j} \times 0.1\hat{k}) = -0.02\hat{i} \text{ N} (towards left).
For wire dcdc: Current is rightwards (i^\hat{i}). F⃗dc=1(0.2i^×0.1k^)=−0.02j^ N\vec{F}_{dc} = 1(0.2\hat{i} \times 0.1\hat{k}) = -0.02\hat{j} \text{ N} (downward).
For wire abab: Current is rightwards (i^\hat{i}). F⃗ab=1(0.2i^×0.1k^)=−0.02j^ N\vec{F}_{ab} = 1(0.2\hat{i} \times 0.1\hat{k}) = -0.02\hat{j} \text{ N} (downward).

Thus, the force is 0.02 N0.02 \text{ N} on each wire; on dada and cbcb towards left, and on dcdc and abab downward.
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