Q127 / 160 · AP EAMCET 2020 (21 Sep Shift 2) · Physics

When a helium nucleus covers a circle of radius \(0.8 \mathrm{~m}\) in \(2 \mathrm{~s}\), find the value of magnetic field \(B\) at the centre of the circle.

  • A
    \(\frac{10^{-19}}{\mu_0} \mathrm{~T}\)
  • Correct answer
    B
    \(\mu_0 \times 10^{-19} \mathrm{~T}\)
  • C
    \(2 \mu_0 \times 10^{-19} \mathrm{~T}\)
  • D
    \(\frac{2 \times 10^{-19}}{\mu_0} \mathrm{~T}\)

Solution

Charge on helium nucleus, \(q=+2 e=2 \times 1.6 \times 10^{-19} \mathrm{C}=3.2 \times 10^{-19} \mathrm{C}\) Radius of helium nucleus, \(r=0.8 \mathrm{~m}\) Time period, \(T=2 \mathrm{~s}\) \(\therefore\) Current associated with helium nucleus, \(I=\frac{q}{T}=\frac{3.2 \times 10^{-19}}{2}=1.6 \times 10^{-19} \mathrm{~A}\) \(\therefore\) Magnetic field at the centre of the loop, \(B=\frac{\mu_0 I}{2 r}=\frac{\mu_0 \times 1.6 \times 10^{-19}}{2 \times 0.8}=\mu_0 \times 10^{-19} \mathrm{~T}\)

Hence, the correct answer is option: 'B'.

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