TS EAMCET · Physics · Magnetic Effects of Current
Three parallel wires a, b and c carrying currents \(i_a, i_b\) and \(i_c\) as shown in the figure are placed next to each other.
The magnitude force on a length \(l\) of the wire a, if \(\mathrm{d}_2=2 \mathrm{~d}_1, i_b=i_a\) and \(i_c=4 i_a\) is
- A \(\frac{\mu_0}{6 \pi \mathrm{d}_1} i_a^2 l\)
- B \(\frac{\mu_0}{2 \pi \mathrm{d}_1} i_a^2 l\)
- C \(\frac{\mu_0}{4 \pi \mathrm{d}_1} i_a^2 l\)
- D \(\frac{\mu_0}{3 \pi \mathrm{d}_1} i_a^2 l\)
Answer & Solution
Correct Answer
(A) \(\frac{\mu_0}{6 \pi \mathrm{d}_1} i_a^2 l\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \left(\frac{\mathrm{F}}{\ell}\right)_{\mathrm{a}}=\frac{\mu_0}{2 \pi} \frac{\mathrm{i}_{\mathrm{a}} \mathrm{i}_{\mathrm{b}}}{\mathrm{d}_1}-\frac{\mu_0}{2 \pi} \frac{\mathrm{i}_{\mathrm{a}} \mathrm{i}_{\mathrm{c}}}{\left(\mathrm{d}_2+\mathrm{d}_1\right)} \\ &…
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