An infinite straight wire carries a current I that varies with time as shown abo
ID: 2120870 • Letter: A
Question
An infinite straight wire carries a current I that varies with time as shown above. It increases from 0 at t = 0 to a maximum value I1 = 2 A at t = t1 = 19 s, remains constant at this value until t = t2 when it decreases linearly to a value I4 = -2 A at t = t4 = 37 s, passing through zero at t = t3 = 30.5 s. A conducting loop with sides W = 37 cm and L = 51 cm is fixed in the x-y plane at a distance d = 51 cm from the wire as shown.
1)
What is the magnitude of the magnetic flux %u03A6 through the loop at time t = t1 = 19 s?
2)
What is %u03B51, the induced emf in the loop at time t = 9.5 s? Define the emf to be positive if the induced current in the loop is clockwise and negative if the current is counter-clockwise.
3)
What is %u03B52, the induced emf in the loop at time t = 21 s? Define the emf to be positive if the induced current in the loop is clockwise and negative if the current is counter-clockwise.
5)
What is %u03B54, the induced emf in the loop at time t = 33.75 s? Define the emf to be positive if the induced current in the loop is clockwise and negative if the current is counter-clockwise.
Please show all steps!! thank you
Explanation / Answer
3. at 21sec, the graph is parallel to time axis .hence slope =0
=> dI/dt=0
emf=- (Uo*w*ln(2))*(dI/dt)/(2*pi)
putting dI/dt=0 ,
we get
emf=0