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Byju's Answer

Standard XII

Physics

Force on a Finite Wire

A pair of sta...

Question

A pair of stationary and infinitely long bent wires are placed in the XY plane as shown in the figure. The wires carry currents of $I = 10$ amp each as shown in the figure. The segments L and M are along the X-axis such that $O S = O R = 0.02$ m. Find the magnitude and direction of the magnetic induction at the origin O.

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Solution

(Refer to Image)
Magnetic field at point $O$ due to the wire $R P$ is
$= \frac{μ_{o}}{4 π} \frac{I}{r} [sin θ_{1} + sin θ_{2}]$
$= \frac{μ_{o}}{4 π} \frac{10}{0.02} \times [sin O^{-} + sin π / 2]$
$= 10^{- 7} \times \frac{10}{0.02} \times 1$

$∴$ Same for the wire $S Q$ .
$∴$ Total $B = \frac{2 \times 10^{- 7} \times 10}{0.02}$

$= 10^{- 7} \times 10 \times 10^{2} = 10^{- 4} T$ .

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(Refer to Image)Magnetic field at point O due to the wire RP is=μo4πIr[sinθ1+sinθ2]=μo4π100.02×[sinO−+sinπ/2]=10−7×100.02×1∴ Same for the wire SQ .∴ Total B=2×10−7×100.02 =10−7×10×102=10−4T .