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PhysicsMultiple correct+4 / -2Question 11 of 54

JEE Advanced 2016 · Paper 1, Physics question 11

A conducting loop in the shape of a right angled isosceles triangle of height 10 cm is kept such that the 90° vertex is very close to an infinitely long conducting wire (see the figure). The wire is electrically insulated from the loop. The hypotenuse of the triangle is parallel to the wire. The current in the triangular loop is in counterclockwise direction and increased at a constant rate of 10 A s−110\ \mathrm{A\,s^{-1}}. Which of the following statement(s) is(are) true?

A long horizontal straight wire (dashed at both ends to show it continues). Just below it hangs a right-angled isosceles triangular loop with its 90° vertex touching the wire and its hypotenuse horizontal, 10 cm below the wire (height marked with a double arrow).
Choose one or more options
Answer and worked solution

Official answer: A, D

Mutual inductance. At distance xx below the wire, the triangle's width is 2x2x. Flux of the wire's field through the loop:
Φ=∫00.1μ0I2πx 2x dx=0.1 μ0πI  ⟹  M=0.1 μ0π.\Phi=\int_0^{0.1}\frac{\mu_0I}{2\pi x}\,2x\,dx=\frac{0.1\,\mu_0}{\pi}I\implies M=\frac{0.1\,\mu_0}\pi.

  • (A) emf in the wire =MdIdt=0.1μ0π×10=μ0π=M\dfrac{dI}{dt}=\dfrac{0.1\mu_0}\pi\times10=\dfrac{\mu_0}\pi V. True.
  • (B) Rotating the loop about the wire does not change MM, by symmetry, so there is no extra emf. False.
  • (C) The counter-clockwise loop current makes flux out of the page through the loop. For the wire's own flux through the loop to oppose the increase (Lenz), the wire current runs left to right. That is the same direction as the hypotenuse current. False.
  • (D) The induced current makes the interaction energy oppose the change, so the force pushes the circuits apart. The side currents next to the wire are antiparallel to it. Repulsive. True.

(A), (D)

Topics:Mutual inductanceForce on a current-carrying conductor
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