Question

. A circular loop of wire originally 10-cm in diameter is oriented perpendicular to a 0.20-T uniform magnetic field. At time t= 0 s one end of the loop of wire is pulled through a small opening the other end such that the circumference of the wire decreases at a constant rate of 5 cm/s. a) If the resistance of the loop is a constant 10Ω, determine the induced current at 1.0s. b) If instead the wire has a constant resistance per meter of 10Ω/m, calculate the induced current. Does it change or remain constant?

Answer 1

a. 0.393A B. Remains constant

Step-by-step explanation:

initial diameter D1= 10cm, New diameter = 5cm ( the rate of reduction is 5cm per sec, so in on sec the diameter would have reduced by 5cm)

initial area of loop = π D²/4= π *10²/4= 78.53cm²

new area of loop after 1 sec = π* 5²/4= 19.6cm²

induced current ∅=
`\int\limits^a_b {B} \, dA` where B is the strength of Magnetic field and A is area, limits a and b are for (area).

induced current ∅=
`\int\limits^(19.6)_(0) {0.02} \, dA`= 0.392A

b. induced current is dependent on the area of loop and the magnitude of magnetic field... a change in resistance wont affect the value of induced current provided the two dependent variables remain constant