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Magnetics question

2022 · 28 Jul · Shift 2 · Q51
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  5. /2022 · 28 Jul · Shift 2 · Q51

Magnetics question

2022 · 28 Jul · Shift 2 · Q51

JEE MainPhysicsMagneticsMCQ+4 / −1
A triangular shaped wire carrying 10 A10 \mathrm{~A}10 A current is placed in a uniform magnetic field of 0.5 T0.5 \mathrm{~T}0.5 T, as shown in figure. The magnetic force on segment CD\mathrm{CD}CD is (Given BC=CD=BD=5 cm\mathrm{BC}=\mathrm{CD}=\mathrm{BD}=5 \mathrm{~cm}BC=CD=BD=5 cm.) JEE Main 2022 (Online) 28th July Evening Shift Physics - Magnetic Effect of Current Question 87 English
  1. A
    0.126 N
  2. B
    0.312 N
  3. C
    0.216 N
  4. D
    0.245 N
View written solutionFree

Correct answer: C

  1. Magnetic force on a straight current-carrying segment

For a straight wire segment in a uniform magnetic field,

F=ILBsin⁡θF = I L B \sin\thetaF=ILBsinθ

where:

  • I=10 AI = 10\,\text{A}I=10A
  • B=0.5 TB = 0.5\,\text{T}B=0.5T
  • L=L =L= length of the segment
  • θ=\theta =θ= angle between the segment and the magnetic field

We need the force on segment CDCDCD.

  1. Geometry of the triangle

Given:

BC=CD=BD=5 cmBC = CD = BD = 5\,\text{cm}BC=CD=BD=5cm

So triangle BCDBCDBCD is an equilateral triangle of side

5 cm=0.05 m5\,\text{cm} = 0.05\,\text{m}5cm=0.05m

Hence each angle is

60∘60^\circ60∘

From the figure, the magnetic field is along side BDBDBD, so the angle between segment CDCDCD and the field is

θ=60∘\theta = 60^\circθ=60∘
  1. Compute the force on segment CDCDCD

Using

F=ILBsin⁡θF = I L B \sin\thetaF=ILBsinθ F=10×0.05×0.5×sin⁡60∘F = 10 \times 0.05 \times 0.5 \times \sin 60^\circF=10×0.05×0.5×sin60∘

Since

sin⁡60∘=32≈0.866\sin 60^\circ = \frac{\sqrt{3}}{2} \approx 0.866sin60∘=23​​≈0.866

So,

F=10×0.05×0.5×0.866F = 10 \times 0.05 \times 0.5 \times 0.866F=10×0.05×0.5×0.866 F=0.25×0.866F = 0.25 \times 0.866F=0.25×0.866 F≈0.2165 NF \approx 0.2165\,\text{N}F≈0.2165N

Thus,

F≈0.216 NF \approx 0.216\,\text{N}F≈0.216N
  1. Match with the options

The correct option is:

C: 0.216 N\boxed{\text{C: } 0.216\,\text{N}}C: 0.216N​
  1. Comparison with stored answer

Stored correct answer: C

Our derived answer: C

So they agree.

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