Time Dependent Current in a Wire

AI Thread Summary
The discussion revolves around calculating the magnetic flux through a conducting loop due to a time-varying current in an infinite straight wire. The current increases to a maximum of 5.2 A at 15 seconds, remains constant, and then decreases to -5.2 A by 26 seconds. The magnetic field is determined using the formula B = μ*I/(2*pi*d), where d is the distance from the wire. The user initially struggles with integrating the flux equation and realizes a mistake related to the integration of 1/x. The correct approach involves properly applying the magnetic flux equation to find the desired value at the specified time.
trolling
Messages
14
Reaction score
0

Homework Statement


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 = 5.2 A at t = t1 = 15 s, remains constant at this value until t = t2 when it decreases linearly to a value I4 = -5.2 A at t = t4 = 26 s, passing through zero at t = t3 = 23 s. A conducting loop with sides W = 27 cm and L = 50 cm is fixed in the x-y plane at a distance d = 57 cm from the wire as shown.What is the magnitude of the magnetic flux Φ through the loop at time t = t1 = 15 s?

Homework Equations



B = μ*I/(2*pi*d)

I = 5.2 A

Φ = ∫B*dA

The Attempt at a Solution



I know I need to use the magnetic flux equation in this somehow. I tried integrating the flux equation above to get something like Φ = ∫B*dA = B*A = ((μ*I)/(2*pi*(((d+L)^2) - (d^2)) * (W*L). (?)

However, when I plugged in the values and typed in what I got into the computer, it didn't like what I had. I tried doing everything I could, & I feel like this is a relatively simple problem. What am I doing wrong?
 

Attachments

  • h17_BfromWire.png
    h17_BfromWire.png
    2.1 KB · Views: 698
Last edited by a moderator:
Physics news on Phys.org
Ignore. I just forgot the integral of 1/x. (ln x)
 
Kindly see the attached pdf. My attempt to solve it, is in it. I'm wondering if my solution is right. My idea is this: At any point of time, the ball may be assumed to be at an incline which is at an angle of θ(kindly see both the pics in the pdf file). The value of θ will continuously change and so will the value of friction. I'm not able to figure out, why my solution is wrong, if it is wrong .
TL;DR Summary: I came across this question from a Sri Lankan A-level textbook. Question - An ice cube with a length of 10 cm is immersed in water at 0 °C. An observer observes the ice cube from the water, and it seems to be 7.75 cm long. If the refractive index of water is 4/3, find the height of the ice cube immersed in the water. I could not understand how the apparent height of the ice cube in the water depends on the height of the ice cube immersed in the water. Does anyone have an...
Back
Top