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Concepts Of Physics MCQ Edition [Volume 2]
Exam
Concepts Of Physics MCQ Edition [Volume 2]
Subject
Physics
Chapter
Magnetic Field due to a Current

Concepts Of Physics MCQ Edition [Volume 2] · Physics · Magnetic Field due to a Current

As shown in the figure, a square loop PQRS carrying a current of...

As shown in the figure, a square loop PQRSPQRS carrying a current of 6.0 A6.0\text{ A} is situated near a long wire carrying 10 A10\text{ A}. Determine the net magnetic force on the square loop.
As shown in the figure, a square loop PQRS carrying a current of 6.0 A is situated near a long wire carrying 10 A .

Options

  1. A2.4×10−5 N2.4 \times 10^{-5}\text{ N} towards right
  2. B3.2×10−5 N3.2 \times 10^{-5}\text{ N} towards right
  3. C1.6×10−5 N1.6 \times 10^{-5}\text{ N} towards right
  4. D1.6×10−5 N1.6 \times 10^{-5}\text{ N} towards left

Correct answer

C. 1.6×10−5 N1.6 \times 10^{-5}\text{ N} towards right

Step-by-step solution

The magnetic force on a straight wire of length LL carrying current I2I_2 placed at a distance rr from a long straight wire carrying current I1I_1 is given by:

F=μ0I1I2L2πrF = \dfrac{\mu_0 I_1 I_2 L}{2\pi r}

The forces on the horizontal segments PQPQ and RSRS are equal and opposite, and their net force is zero.

For the side SPSP of the square loop:
The current in SPSP is downwards, which is anti-parallel to the current in the long wire. Therefore, the force on SPSP is repulsive (towards the right).
Distance r1=1 cm=0.01 mr_1 = 1\text{ cm} = 0.01\text{ m}
Length L=2 cm=0.02 mL = 2\text{ cm} = 0.02\text{ m}
FSP=4π×10−7×10×6×0.022π×0.01=2.4×10−5 NF_{SP} = \dfrac{4\pi \times 10^{-7} \times 10 \times 6 \times 0.02}{2\pi \times 0.01} = 2.4 \times 10^{-5}\text{ N} (towards right)

For the side RQRQ of the square loop:
The current in RQRQ is upwards, which is parallel to the current in the long wire. Therefore, the force on RQRQ is attractive (towards the left).
Distance r2=1 cm+2 cm=3 cm=0.03 mr_2 = 1\text{ cm} + 2\text{ cm} = 3\text{ cm} = 0.03\text{ m}
FRQ=4π×10−7×10×6×0.022π×0.03=0.8×10−5 NF_{RQ} = \dfrac{4\pi \times 10^{-7} \times 10 \times 6 \times 0.02}{2\pi \times 0.03} = 0.8 \times 10^{-5}\text{ N} (towards left)

The net magnetic force on the loop is:
Fnet=FSP−FRQ=2.4×10−5−0.8×10−5=1.6×10−5 NF_{net} = F_{SP} - F_{RQ} = 2.4 \times 10^{-5} - 0.8 \times 10^{-5} = 1.6 \times 10^{-5}\text{ N}

Since FSP>FRQF_{SP} > F_{RQ}, the net force is directed towards the right.
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