A half-infinite wire carries current I from negative infinity to the origin, where it builds up at a point charge with increasing q (so dq/dt = I). Consider the circle shown in which has radius b and subtends an angle 2θ with respect to the charge. If θ=600, then find ∮B→.dl→ in the given circle. If your answer is μ0IK, then write K = ?

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A half-infinite wire carries current $I$ from negative infinity to the origin, where it builds up at a point charge with increasing q (so dq/dt = I). Consider the circle shown in which has radius b and subtends an angle $2 θ$ with respect to the charge. If $θ = 60^{0},$ then find $\oint \vec{B} . \vec{d l}$ in the given circle. If your answer is $\frac{μ_{0} I}{K},$ then write K = ?

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answer is 4.

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Detailed Solution

$μ_{0} \in_{0} \int_{S} \frac{\partial E}{\partial t} . d a = μ_{0} \in_{0} \frac{\partial}{\partial t} \int_{S} E . d a = μ_{0} \in_{0} \frac{\partial Φ}{\partial t} = μ_{0} \in_{0} \frac{d q / d t}{2 \in_{0}} (1 - \cos θ) = \frac{μ_{0} I}{2} (1 - \cos θ)$