An infinite wire placed along z-axis, has current $ \mathrm{I}_{1} $ in positive z-direction. A conducting rod placed in xy plane parallel to y- axis has current $ \mathrm{I}_{2} $ in positive y-direction. The ends of the rod subtend angles of $ +30^{\circ} $ and $ -60^{\circ} $ at the origin with positive $ \mathrm{x}- $ direction. The rod is at a distance 'a' from the origin. Find net force on the rod.

Question

An infinite wire placed along z-axis, has current $ \mathrm{I}_{1} $ in positive z-direction. A conducting rod placed in xy plane parallel to y- axis has current $ \mathrm{I}_{2} $ in positive y-direction. The ends of the rod subtend angles of $ +30^{\circ} $ and $ -60^{\circ} $ at the origin with positive $ \mathrm{x}- $ direction. The rod is at a distance 'a' from the origin. Find net force on the rod., $ \mathrm{F}=\frac{\mu_{0}}{4 \pi} \mathrm{I}_{1} \mathrm{I}_{2} \ell \ln 3(-\widehat{\mathrm{k}}) $, $ \mathrm{F}=\frac{\mu_{0}}{4 \pi} 2 \mathrm{I}_{1} \mathrm{I}_{2} \ell \mathrm{n} 3(-\widehat{\mathrm{k}}) $, $ \mathrm{F}=\frac{\mu_{0}}{4 \pi} \mathrm{I}_{1} \mathrm{I}_{2} \ell \mathrm{n} 3(\widehat{\mathrm{k}}) $, $ \mathrm{F}=\frac{\mu_{0}}{4 \pi} 2 \mathrm{I}_{1} \mathrm{I}_{2} \ell \mathrm{n} 3(\widehat{\mathrm{k}}) $

MARKS App · Accepted Answer

x a = tan θ x = a tan θ 1 d x = a sec 2 θ d θ B = μ 0 4 π 2 I 1 r · · · 2 d F → = I 2 dx B sin θ - k ^ · · · 3 From (1), (2) & (3) d F → = I 2 asec 2 θdθ μ 0 4 π 2 I 1 asecθ s i n θ ( − k ^ ) = μ 0 4 π 2 I 1 I 2 s i n θsecθ d θ ( − k ^ ) F = μ 0 2 π I 1 I 2 ∫ - 60 ° 30 ° s i n θsecθ d θ ( − k ^ ) F = μ 0 2 π I 1 I 2 lncos θ 30 ° - 60 ° ( k ^ ) ⇒ F = μ 0 4 π I 1 I 2 ℓ n 3 - k ^

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