The capacitor in the figure is charged to 50 V . The switch closes at t=0 s . I

Question

The capacitor in the figure is charged to 50 V . The switch closes at t=0 s .

I can't seem to be able to upload a diagram of the circuit, but there is a 2.0 UF capacitor, a 5.0 ohm resistor, and a point indicated 1.0 cm away from the circuit.


*Draw a graph showing the magnetic field strength as a function of time at the position of the dot. On your graph indicate the maximum field strength and provide an appropriate numerical scale on the horizontal axis.

I have this much that I know is correct, i just am not sure how to find points to plot an exponential graph with other than the maximum field strength at the position of the dot is 4.0*10^-4. Which I found from the equation B=u0I/2r. I have no idea how to plot the exponential curve though. for instance if 4.0*10^-4 T is the maximum point how can I find the point at 10 us and 20us or 30us? I am not sure how to explain it, but i am really confused and any help would be greatly appreciated.

Explanation / Answer

I am getting a different number for max field (but I cannot see the diagram). I am getting 2*10^-4T for a point 0.01m away. But I digress,

The current from a discharging capacitor is

I = Vo/R (e-t/RC)

So the magnetic field at this point would be:

B = o/2 [Vo/R (e-t/RC)]/r

Subsituting some numbers in from your problem:

B = o/2 [(50V/5)* e-t/(2.0*10^-6F * 5)]/0.01m

So simplifying;

B = o/2 [1000 e-t/(1*10^-5)]

Putting the right values for o/2 makes it

B = (2*10^-4 T)e-t/(1*10^-5)

Notice the first value (for t=0) is your max field. If you are sure that the max field at your point is 4*10^-4 T, then use that instead of what I have.

Use this function to get your other points

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