What Is the Correct Current Equation to Induce Given Flux in a Circuit?

[Sarah0001]

1. Problem Statement:
flux in a flux circuit varies according to the equation Φ = sin ωt.
Using a constant k, what is the equation for a current which could induce the flux in the flux circuit above?

Homework Equations

Φ = sin ωt.

The answer given is :

The Attempt at a Solution

My attempt at this solution is, that Current that induces the flux (regardless of whether the flux varies or not due to current) and is directly proportional to the flux as a result . Flux and current are in phase is my understanding (correct me if I'm wrong).

Thus. I = Ksinwt
however the answer gives -Ksinwt, I am confused on how they get the -ve

I know Emf induced and thus the current induced are proportional to the (-ve) rate of change of flux linkage,

however the question asks for a current which would induce the flux, not the other way round (where only a change of flux could only induce current) ,

hence it would be solely a proportional relationship between current and flux (flux dependent on current),
so surely the answer is Ksinwt as nothing is being opposed - I am unsure what the negative is indicating here about the current if the answer given is correct.

 

[berkeman]

Look for an equation that relates the flux through a wire loop versus the current flowing through the loop. If you drive a sinusoidal current through a wire loop, what is the equation for the flux as a function of time through the loop's area?

 

[Sarah0001]

Look for an equation that relates the flux through a wire loop versus the current flowing through the loop. If you drive a sinusoidal current through a wire loop, what is the equation for the flux as a function of time through the loop's area?

Hi, thank you for your response. I am unsure what what equation that would be and how it helps to solve the question.