When a helium nucleus covers a circle of radius \(0.8 \mathrm{~m}\) in \(2 \mathrm{~s}\), find the value of…
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.
\(\frac{10^{-19}}{\mu_0} \mathrm{~T}\)
\(\mu_0 \times 10^{-19} \mathrm{~T}\)
\(2 \mu_0 \times 10^{-19} \mathrm{~T}\)
\(\frac{2 \times 10^{-19}}{\mu_0} \mathrm{~T}\)
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,
\(B=\frac{\mu_0 I}{2 r}=\frac{\mu_0 \times 1.6 \times 10^{-19}}{2 \times 0.8}=\mu_0 \times 10^{-19} \mathrm{~T}\)