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

NTA Abhyas 2020 · Physics · Electromagnetic Induction

A uniform metal rod is moving with a uniform velocity v parallel to...

A uniform metal rod is moving with a uniform velocity vv parallel to a long straight wire carrying a current II. The rod is perpendicular to the wire with its ends at distances r1{r}_{1} and r2{r}_{2} (with r2>r1{r}_{2} > {r}_{1}) from it. The E.M.F. induced in the rod at that instant is

Options

  1. Azero
  2. Bμ0Iv2πln⁡(r2r1)\dfrac{{μ}_{0}Iv}{2\pi}\ln \left(\dfrac{r2}{r1}\right)
  3. Cμ0Iv2πln⁡(r1r2)\dfrac{{μ}_{0}Iv}{2\pi}\ln \left(\dfrac{r1}{r2}\right)
  4. Dμ0Iv4π(1−r1r2)\dfrac{{μ}_{0}Iv}{4\pi} \left(1 - \dfrac{r1}{r2}\right)

Correct answer

B. μ0Iv2πln⁡(r2r1)\dfrac{{μ}_{0}Iv}{2\pi}\ln \left(\dfrac{r2}{r1}\right)

Step-by-step solution

B = \dfrac{{μ}_{0}i}{2\pi x}<br/><br/><br /><br />dε = Bv \left(dx\right)<br/><br/><br /><br />ε = \dfrac{{μ}_{0}iv}{2\pi}\mathop{∫}_{r2}^{r1}\dfrac{dx}{x} =\left(\dfrac{{μ}_{0}iv}{2\pi}ln\dfrac{r2}{r1}\right)
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