- #1
ElijahRockers
Gold Member
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1. The problem.
A circular loop of radius 4cm has a plane which is perpendicular to the electric field B. (The area vector is +k, so is the field vector.) The strength of the field varies with time according to the equation B=4/(t^3). Give an expression for the voltage as a function of time.
2. Homework Equations .
OK, I'm using V_induced = -d/dt(B_flux), which is Faraday's law, and B_flux = Integral(B.dA)
I'm not great at this calculus stuff, but when trying to find the field flux, int(B.dA), I can assume that dA is equal to A, and that it's constant, since the area is not changing right? Well A = .04m^2, so I get B_flux = .04*int(4/(t^3))dt, right? Are my limits of integration from 0 to DeltaT? Either way, I get an error because the integral will leave me with t in the denominator, and since the initial limit is 0, it is undefined.
Anyway, after I do find an expression for the B_flux, i can take the derivative of it to find d/dt(B_flux) and that should be the Induced voltage as a function of time... right?
Thanks in advance.
A circular loop of radius 4cm has a plane which is perpendicular to the electric field B. (The area vector is +k, so is the field vector.) The strength of the field varies with time according to the equation B=4/(t^3). Give an expression for the voltage as a function of time.
2. Homework Equations .
OK, I'm using V_induced = -d/dt(B_flux), which is Faraday's law, and B_flux = Integral(B.dA)
The Attempt at a Solution
I'm not great at this calculus stuff, but when trying to find the field flux, int(B.dA), I can assume that dA is equal to A, and that it's constant, since the area is not changing right? Well A = .04m^2, so I get B_flux = .04*int(4/(t^3))dt, right? Are my limits of integration from 0 to DeltaT? Either way, I get an error because the integral will leave me with t in the denominator, and since the initial limit is 0, it is undefined.
Anyway, after I do find an expression for the B_flux, i can take the derivative of it to find d/dt(B_flux) and that should be the Induced voltage as a function of time... right?
Thanks in advance.