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A straight conducting wire of length l carries a current I. This wire is bent into the shape of a semicircular loop (with two straight ends connecting the diameter). The magnetic moment of this loop is expressed in the form (pi * I / P) * (l / (pi + K))². Find the value of P + K.
- 2
- 3
- 4
- 5
Correct answer: 3
Solution
The radius is r = l/(pi+2). Magnetic moment M = I * (pi*r²/2) = (pi*I/2)*(l/(pi+2))², giving P=2, K=2, so P+K=4. Wait — recheck: M = I*A = I*(pi*r²/2) = (pi*I/2)*(l/(pi+2))². Comparing with pi*I/P*(l/(pi+K))² gives P=2, K=2, so P+K=4.
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