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NTA Abhyas 2020
Exam
NTA Abhyas
Year
2020
Subject
Physics
Chapter
Electromagnetic Induction

NTA Abhyas 2020 · Physics · Electromagnetic Induction

A wire bent as a parabola y = kx ^ 2 is located in a uniform...

A wire bent as a parabola y=kx2y = {kx}^{2} is located in a uniform magnetic field of induction BB, the vector BB being perpendicular to the plane xyxy. At t=0t = 0, the sliding wire starts sliding from the vertex OO with a constant acceleration a linearly as shown in Fig. Find the emf induced in the loop -

A wire bent as a parabola y = kx ^ 2 is located in a uniform magnetic field of induction B , the vector B being

Options

  1. ABy2akBy\sqrt{\dfrac{2a}{k}}
  2. BBy4akBy\sqrt{\dfrac{4a}{k}}
  3. CBy8akBy\sqrt{\dfrac{8a}{k}}
  4. DByakBy\sqrt{\dfrac{a}{k}}

Correct answer

C. By8akBy\sqrt{\dfrac{8a}{k}}

Step-by-step solution

A wire bent as a parabola y = kx ^ 2 is located in a uniform magnetic field of induction B , the vector B being

dϕ=B.dA=2Bxdyandy=kx2dϕ = B . dA = 2Bxdy and y = {kx}^{2}

∴x=yk∴ x = \sqrt{\dfrac{y}{k}}

∴EmfE=dϕdt=2Bykdydt∴ Emf E = \dfrac{dϕ}{dt} = 2B\sqrt{\dfrac{y}{k}}\dfrac{dy}{dt}

using v2=2asv^{2} = 2as

dydt=v=2ay\dfrac{dy}{dt} = v = \sqrt{2ay}

or   \left|ε\right| = \dfrac{dϕ}{dt} = 2B\sqrt{\dfrac{y}{k}}\sqrt{2ay}<br/><br/>or   ∣ε∣=By8ak<br /><br />or   \left|ε\right| =By\sqrt{\dfrac{8a}{k}}
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