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JEE Main 2014 (9 Apr, Shift 1) · Field of a Magnet & Magnet in a Uniform Field

Field of a Magnet & Magnet in a Uniform Field question from JEE Main 2014 (9 Apr, Shift 1)

Q21JEE Main 2014 · 9 APR · SHIFT 1Medium

Field of a Magnet & Magnet in a Uniform Field

The mid points of two small magnetic dipoles of length d in end-on positions, are separated by a distance x, (x > > d). The force between them is proportional to x−-n where n is:

Figure

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Answer: (d)

  1. Field of the first dipole on its axis: B=μ04π2m1x3B = \dfrac{\mu_0}{4\pi}\dfrac{2m_1}{x^3}.
  2. Force on the second dipole along the axis: F=m2dBdx=μ04π6m1m2x4F = m_2\dfrac{dB}{dx} = \dfrac{\mu_0}{4\pi}\dfrac{6m_1m_2}{x^4}
  3. So F∝x−4F \propto x^{-4} and the answer is (d) n=4n = 4.
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