First slide

Applications involving charged particles moving in a magnetic field

Question

Two circular loops are parallel, coaxial, and almost in contact, 1.00 mm apart, Each loop is 10.0 cm in radius. The top loop carries a clock wise current of 140 A. The bottom loop carries a counterclockwise current of 140 A. Calculate the magnetic force exerted by the bottom loop on the top loop.

Difficult

Solution

Model the two wires as straight parallel wires.
$F_{B} = \frac{μ_{0} I^{2} l}{2 π a} w h e r e l = p e r i m e t e r o f l o o p a n d a = d i s \tan c e b e t w e e n l o o p s \Rightarrow F_{B} = \frac{(4 π \times 10^{- 7}) {(140)}^{2} (2 π) (0.1)}{2 π (1.00 \times 10^{- 3})} = 2.46 N$

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