磁束 / Magnetic Flux

Two problems regarding Magnetic Flux.

1) Find the induced current of the loop of wire below:

Given:

r = 10.0 cm
B = From 1 T to 5T
N = 15
Δt = 10s
R = 10 Ω

This question is easily answered using Faraday's Law and Ohm's Law.

Faraday's Law:


ε = -NΔΦ_m / Δt
Φm = BAcosθ

ε = -(15*(5-1)πr^2cos30) / 10
ε = -15π(0.10)^2 * √3/2 * 4/10
ε = 0.0290757133 V

Ohm's Law:

ε = IR
I = ε/R

I = 0.0290757133 / 10
I = 0.0029075713 A

2) Find the induced force on the orange bar.

 l = Length
B = Magnetic Field

No numbers given, so we are finding a general solution. Once again, use Faraday's Law and Ohm's Law:

a) ε = IR

b) ε = ΔΦ_m / Δt = BΔA / Δt = BlΔx / Δt = Blv


Equate a and b:

IR = Blv
I = Blv / R


Finally:


F = IlB = Blv / R * I * B
F = B^2l^2v / R