Questions

Two infinitely long straight parallel wires carry equal currents ‘i’ in the same direction and are 2 m apart. Magnetic induction at a point which is at same normal distance $\sqrt{2}\mathrm{m}$ from each wire has magnitude

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a

μ0i2π2

b

μ0i4π2

c

μ0i22π

d

μ0i2π

detailed solution

Correct option is D

In three dimensional space, the point lies perpendicular to the plane containing wires. Let θ be the half-angle made by position vector of particle with vertical. Thensinθ=12⇒θ=45° If field due to each wire is BBnet =2Bcosθ Bnet =2μ0i2π212=μ0i2π

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Two circular coils X and Y, having equal number of turns and carrying currents in the same sense, subtend same solid angle at point O. If the smaller coil X is midway between O and Y and if we represent the magnetic induction due to bigger coil Y at O as B_{y} and that due to smaller coil Y at O as B_{x}, then find the ratio B_{x}/B_{y}.

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