A rigid wire loop of square shape having side of length L and resistance R is moving along the x-axis with a constant velocity v 0 in the plane of the paper. At t = 0, the right edge of the loop enters a region of length 3L where there is a uniform magnetic field B 0 into the plane of the paper, as shown in the figure. For sufficiently large v 0 , the loop eventually crosses the region. Let x be the location of the r

Step-by-step solution

When loop was entering (x ϕ = B L x e = d ϕ d t = - B L d x d t e = B L V i = e R = B L V R A C W F = i B (Left direction) = B 2 L 2 V R (in left direction) ⇒ a = F m = B 2 L 2 V m R a = V d V d x V d V d x = B 2 L 2 V m R ⇒ ∫ V 0 V d V = - B 2 L 2 m R ∫ 0 x d x ⇒ V = V 0 - B 2 L 2 m R x (straight line of negative slope for x I = B L R V ⇒ (I vs x will also be straight line of negative slope for x L ≤ x ≤ 3 L d ϕ d t = 0 e = 0 i = 0 F = 0 x > 4 L e = B l v Force also will be in left direction. i = B L W R (clockwis