A rectangular conducting loop of length 4cm and width 2cm is in the xy -plane, as shown in the figure. It is being moved away from a thin and long conducting wire along the direction $\frac{\sqrt{3}}{2} \hat{x} + \frac{1}{2} \hat{y}$ with a constant speed v. The wire is carrying a steady current $I = 10 A$ in the positive x-direction. A current of 10 $μ$ A flows through the loop when it is at a distance d=4 cm from the wire. If the resistance of the loop is 0.1Ω, then the value of v is _______ ms⁻¹.
[Given: The permeability of free space $μ_{0} = 4 π \times 10^{- 7} {NA}^{- 2}]$

Question

A rectangular conducting loop of length 4cm and width 2cm is in the xy -plane, as shown in the figure. It is being moved away from a thin and long conducting wire along the direction $\frac{\sqrt{3}}{2} \hat{x} + \frac{1}{2} \hat{y}$ with a constant speed v. The wire is carrying a steady current $I = 10 A$ in the positive x-direction. A current of 10 $μ$ A flows through the loop when it is at a distance d=4 cm from the wire. If the resistance of the loop is 0.1Ω, then the value of v is _______ ms⁻¹.
[Given: The permeability of free space $μ_{0} = 4 π \times 10^{- 7} {NA}^{- 2}]$

Infinity Learn · Accepted Answer

Induced emf depends on velocity along y axisTotal induced emf is VyB1l−VyB2l=ε⇒VylB1−B2=ε⇒V⋅sin⁡θB1−B2l=ε⇒v2B1−B2l=ε⇒v2μ0i2πd1−μ0i2πd2l=ε ⇒vμoil4π1d1−1d2=εNow i , Putting thevalues we get v=4

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