A rectangular coil with N = 9,000 turns that has a resistance of 3.70 Ohms is co
ID: 1838090 • Letter: A
Question
A rectangular coil with N = 9,000 turns that has a resistance of 3.70 Ohms is coplanar with a long wire which carries a current which depends on time according to I0 *exp(-t/tau), where I0 = 9.00 A and tau = 7.20 s. The rectangular loop has a width of W = 1.20 cm and length L = 4.80 cm. The near side of the loop is a distance D = 6.10 cm from the wire.
What is the magnetic flux in ONE turn of the coil at t = 3.20 s?
What is the ?mf in the entire coil at t = 3.20 s? For the purposes of entering a sign, let the positive direction for the ?mf in the loop be in the clockwise direction.
What is the power dissipated in the entire coil at t = 3.20 s?
What is the total energy dissipated in the entire coil from t = 0 to t = 3.20 s?
Explanation / Answer
I = 9 exp(-t/7.2)
Flux in the coil = F
consder element dx at diatance x from the long wire st D<x<D + w
then dF = BdA = 2kILdx/x
Net flux = 2kILln([D+w]/D) = 2*10^-7*I*0.048*ln(0.073/0.061) = 1.5516*10^-8 exp(-t/7.2)
a) at t = 3.2 s
V = 0.994855*10^-8 V
b) for 9000 turns
at t = 3.2 s, V = 8.95699 *10^-5 V (+ve because clockwise emf is generated)
c) Power = V^2/R = 2.1667e-9 W
d) Total Energy = E
Energy at time t, dE = V^2dt/R = 5.27e-9 exp(-2t/7.2) dt
Integrating from t = 0 to t = 3.2 s
E = 5.27e-9[1 - exp(-2*3.2/7.2) ]* 7.2 / 2 = 1.117*10^-8 J