Question

A rectangular coil with resistance R has N turns, each of length l and width w as shown in Figure P20.25. The coil moves into a uniform magnetic field with constant velocity . What is the magnitude and direction of the total magnetic force on the coil during the following intervals? (Use N, B, w, l,v, and R as needed.)

(a) as it enters the magnetic field

(b) as it moves within the field

(c) as it leaves the field

Answer 1

If the coil is enters the magnetic field region then there isincrese in the magnetic flux through the coil and hence induced emfis E = df/dt = d/dt(NBA) =d/dt(NBwdx) = NBwv
v = speed of the coil '
w = width of the coil
N = number of turns of the coil
B = magnetic field
Then induced current I = E/R = NBwv/R
R = resistance of the coil
Then net force on the coil when it is entering the magneticfield is F = BI(Nw)
F = B( NBwv/R )*(Nw) = N2B2w2v/R andthe direction is towards left.
b) As it moves in the magnetic field then there is no changein magnetic flux and hence no induced emf and hence noinduced current and no net magnetic forcethat is0 N .
c) As it leaves the field net force on the coilwhen it is entering the magnetic field is F = BI(Nw)
F = B( NBwv/R )*(Nw) = N2B2w2v/R andthe direction is towards left