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JEE Main 20206 SeptemberEvening Shift
Exam
JEE Main
Year
2020
Date
6 September
Shift
Evening Shift
Subject
Physics
Chapter
Magnetic Effects of Current

JEE Main 2020 · 6 September · Evening Shift · Physics · Magnetic Effects of Current

A square loop of side 2a and carrying current I is kept in xz plane...

A square loop of side 2a2a and carrying current II is kept in xzxz plane with its centre at origin. A long wire carrying the same current II is placed parallel to zz-axis and passing through point \left(0, b, 0\right), \left(b > > a\right). The magnitude of torque on the loop about zz-axis will be :A square loop of side 2a and carrying current I is kept in xz plane with its centre at origin. A long wire carrying theA square loop of side 2a and carrying current I is kept in xz plane with its centre at origin. A long wire carrying the

Options

  1. A2μ0I2a2πb\dfrac{2{\mu}_{0}{I}^{2}{a}^{2}}{\pi b}
  2. B\dfrac{2{\mu}_{0}{I}^{2}{a}^{2}b}{\pi\left({a}^{2} + {b}^{2}\right)}
  3. C\dfrac{{\mu}_{0}{I}^{2}{a}^{2}b}{2\pi\left({a}^{2} + {b}^{2}\right)}
  4. Dμ0I2a22πb\dfrac{{\mu}_{0}{I}^{2}{a}^{2}}{2\pi b}

Correct answer

B. \dfrac{2{\mu}_{0}{I}^{2}{a}^{2}b}{\pi\left({a}^{2} + {b}^{2}\right)}

Step-by-step solution

A square loop of side 2a and carrying current I is kept in xz plane with its centre at origin. A long wire carrying the

Net force acting on wire ABAB & CDCD are zero

A square loop of side 2a and carrying current I is kept in xz plane with its centre at origin. A long wire carrying the

τ=F1cosθ×2a=μ02πi2a2+b2(2a)×ba2+b2×2aτ = {F}_{1}cos \theta \times 2a = \dfrac{{\mu}_{0}}{2\pi}\dfrac{{i}^{2}}{\sqrt{{a}^{2} + {b}^{2}}} ( 2a ) \times \dfrac{b}{\sqrt{{a}^{2} + {b}^{2}}} \times 2a

τ=2μ0.i2a2bπ(a2+b2)τ = \dfrac{2{\mu}_{0} . {i}^{2}{a}^{2}b}{\pi\left({a}^{2} + {b}^{2}\right)}

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