Coil placed in a time-varying magnetic field

AI Thread Summary
A coil with a radius of 3.75 cm and 500 turns is placed in a time-varying magnetic field defined by B = (1.20 x 10^-2 T/s)t + (2.70 x 10^-5 x 4)t^4. The coil is connected to a 610-Ω resistor, and the induced current is calculated using the equations ε = N d/dt(BA) and I = ε/R. The user initially calculated the emf correctly but received an incorrect current value when substituting time t0 = 5.50s. There is confusion regarding the interpretation of the variable x in the magnetic field equation and whether the second term should be treated differently. Clarification on the equation's variables and proper application of time in the calculations is needed to resolve the discrepancies.
PKay
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Homework Statement


A coil 3.75cm radius, containing 500 turns, is placed in a uniform magnetic field that varies with time according to B = (1.20 x 10-2 T/s)t + (2.70 x 10-5x4)t4. The coil is connected to a 610-Ω resistor, and its plane is perpendicular to the magnetic field. You can ignore the resistance of the coil. What is the current in the resistor at time t0 = 5.50s ?

Homework Equations


ε = N d/dt(BA)
I = ε/R

The Attempt at a Solution


First I looked for the emf using the first equation and when I put it into mastering physics, I got it right (0.0265 +0.000265 t3. Then, I used the second equation to get the induced current. I plugged 5.50s into the emf equation and then divided by R. I got 1.16 x 10-4. I can't figure out why it's saying my answer is wrong. I also put in 1.15 x 10-4 also just in case masteringphysics likes just truncating the answer. However, that was also wrong. Does it have something to do with t being the initial time and not the final time? If so, I'm not really sure how to proceed from there.
 
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Hi PKay. I'm just wondering what is x in your equation?
 
Assuming the second term in B is 2.7e-5 t^4 I don't get 0.000265 t^3 for the second term in the emf.
 

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