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Four long parallel conductors carry equal currents of $5.0 A$ . The direction of the current is into the page at points $A$ and $B$ and out of the page at $C$ and $D$ . Calculate the magnitude and direction of the magnetic field at point $P$ , located at the centre of the square.
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$20.0 μ T$ towards bottom of the square

$30.0 μ T$ towards bottom of the square

$20.0 μ T$ towards top of the square

$30.0 μ T$ towards top of the square

answer is A.

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Detailed Solution

$B_{A} = B_{B} = B_{C} = B_{D} = B = \frac{μ_{0}}{2 π} \frac{i}{r} = \frac{(2 \times 10^{- 7}) (5)}{(\frac{0.2}{\sqrt{2}})} = (5.0 \sqrt{2}) \times 10^{- 6} T$

Net magnetic field $= \sqrt{{(B_{A} + B_{C})}^{2} + {(B_{B} + B_{D})}^{2}} = 2 \sqrt{2} B$

$= 2.0 \times 10^{- 5} T$ (towards bottom as shown)

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