A rectangular loop with sides of length a= 1.00 cm and b= 4.60 cm is placed near

Question

A rectangular loop with sides of length a= 1.00 cm and b= 4.60 cm is placed near a wire that carries a current that varies as a function of time:
i(t)=3.62+1.27t2
where the current is in Amperes and the time is in seconds. The distance from the straight wire to the closest side of the loop is d= 0.580 centimeters.

What is the magnetic flux through the loop at time t= 1.10 seconds? (Define positive flux into the page.)

A rectangular loop with sides of length a= 1.00 cm and b= 4.60 cm is placed near a wire that carries a current that varies as a function of time: i(t)=3.62+1.27t^2 where the current is in Amperes and the time is in seconds. The distance from the straight wire to the closest side of the loop is d= 0.580 centimeters. What is the magnetic flux through the loop at time t= 1.10 seconds? (Define positive flux into the page.)

Explanation / Answer

given i = 3.62 + 1.27 t^2

i at t = 1.1 is

i = 3.62 + (1.27 * 1.1*1.1)

i = 5.1567 Amps

apply magnetic field due to st wire B = uoi/2piR

B = 4*3.14 e-7 * 5.1567/(2*3.14 * 0.0058)

B = 1.77 e-4 tesla

so

now use the formula for magnetic flux phi = NAB

flux = 1 * 1.77 e-4 * 0.01* 0.046

flux = 8.142 e-8 Wb

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