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: 696
Last edited by a moderator:
Physics news on Phys.org
Ignore. I just forgot the integral of 1/x. (ln x)
 
Thread 'Collision of a bullet on a rod-string system: query'
In this question, I have a question. I am NOT trying to solve it, but it is just a conceptual question. Consider the point on the rod, which connects the string and the rod. My question: just before and after the collision, is ANGULAR momentum CONSERVED about this point? Lets call the point which connects the string and rod as P. Why am I asking this? : it is clear from the scenario that the point of concern, which connects the string and the rod, moves in a circular path due to the string...
Thread 'A cylinder connected to a hanged mass'
Let's declare that for the cylinder, mass = M = 10 kg Radius = R = 4 m For the wall and the floor, Friction coeff = ##\mu## = 0.5 For the hanging mass, mass = m = 11 kg First, we divide the force according to their respective plane (x and y thing, correct me if I'm wrong) and according to which, cylinder or the hanging mass, they're working on. Force on the hanging mass $$mg - T = ma$$ Force(Cylinder) on y $$N_f + f_w - Mg = 0$$ Force(Cylinder) on x $$T + f_f - N_w = Ma$$ There's also...
Back
Top