A rectangular conducting loop of length 4 cm and width 2 cm is in the x y -plane, as shown in the figure. It is being moved away from a thin and long conducting wire along the direction 3 2 x ∧ + 1 2 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 t

Step-by-step solution

The two sides of the rectangular loop which are perpendicular to the wire would not contribute in induced emf. Angle of velocity vector with x-axis is tan α = 1 2 3 2 = 1 3 . Therefore, α = 30 ° . For parallel sides: E → = B → × v → = μ 0 I 2 π x × v ⇒ Net emf = E 1 cos 60 o - E 2 cos 60 o × width = 1 2 × 2 100 × μ 0 I v 2 π 1 4 100 - 1 8 100 = 1 100 × 2 × 10 - 7 × 10 × v × 100 8 = 2 . 5 v × 10 - 7 Now,