The dimensions of the rectangular loop of wire in (Figure 1) are ? = 400 mm and
ID: 2032799 • Letter: T
Question
The dimensions of the rectangular loop of wire in (Figure 1) are ? = 400 mm and w = 120 mm. The mass of the loop is 30 g , its resistance is 7.0 V/A ,and before entering the magnetic field shown the loop is moving at a constant speed vi. The magnetic field magnitude is 5.0 T, and the loop's area vector is parallel to the field direction.
a)How many seconds after the leading edge of the loop enters the magnetic field is the loop's speed half its initial value? Ignore any friction effects.
B into the figure ?Explanation / Answer
let t be the time at which one side of the loop is inside the magnetic field and moving with
the velocity v m/s
indued emf e = V B W
W is angualr velocity
Induced current i = emf/R
i = V B W/R
R is resistance
Force on side = iB L = B^2 W^2 V/R
also as Force F= ma
a = F/m
a = -B^2 W^2 V/mR
so
a = dV/dt = -B^2 W^2 V/mR
1/v dv/dt = - B^2 W^2/mR
integrating on both sides
intg of 1/v dv/dt = - B^2 W^2/mR
ln (v) = - B^2 W^2 t/mR
t = mR ln2/B^2 W^2
t = 0.03 * 7 * ln2 /(5^2* 0.120^2)
t = 0.404 secs