As shown in the figure, two infinitely long, identical wires are bent by \(90^o\) and placed in such a way that the segments \(LP\) and \(QM\) are along the \(x-\) axis, while segments \(PS\) and \(QN\) are parallel to the \(y-\) axis. If \(OP = OQ = 4\, cm\), and the magnitude of the magnetic field at \(O\) is \(10^{-4}\, T\), and the two wires carry equal current (see figure), the magnitude of the current in each wire and the direction of the magnetic field at \(O\) will be \((\mu_ 0 = 4\pi \times10^{-7}\, NA^{-2})\)

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Answer & Solution

Correct Answer

(C) \(20\, A\), perpendicular into the page

Detailed explanation

\(B=2\left[\frac{\mu_{0} i}{4 n d}\left(\cos \theta_{1}-\cos \theta_{2}\right)\right]\)

\(B=10^{-4} \quad \theta_{1}=90^{\circ}\)

\(\mu_{0}=4 \pi \times 10^{-7} \quad \theta_{2}=180^{\circ}\)

\(d=4 \times 10^{-2}\)

\(\Rightarrow \mathrm{i}=20\, \mathrm{A}\) (into the page)

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