# Induced emf and current

#### themoleculoma

1. The problem statement, all variables and given/known data

Resistance = R
Angle = theta
B = 2cos(2t)
Circular wire loop where magnetic field acts at theta degrees with respect to the normal of the wire loop.
Find induced current and emf in wire loop. Find induced electric field at radial distance d from center of wire loop.

2. Relevant equations

$$\epsilon$$ = -d$$\Phi$$/dt
I = $$\epsilon$$/R

3. The attempt at a solution

A = $$\pi$$r$$^{}2$$
$$\epsilon$$ = d(BA)/dt
= A dB/dt
= $$\pi$$r$$^{}2$$ d(2cos(2t))/dt
= -4$$\pi$$r$$^{}2$$ sin(2t) = induced emf (area not changing)

Given a magnetic field B with a constraint of 2t for $$\omega$$t, and no time, the answer must be with respect to t, correct? You can't use the frequency given by 2/2pi can you?

i = $$\epsilon$$ / R
i = -4$$\pi$$r$$^{}2$$ sin(2t) / R

Since I still don't know time I'm guessing I have to solve as a function of t?

$$\epsilon$$ = dB/dt d/2 = -2sin(2t)d

Related Introductory Physics Homework News on Phys.org

#### Delphi51

Homework Helper
There should be a sin(theta) or cos(theta) in the expression for emf because only the part of B that is perpendicular to the coil causes emf.

Other than that, your calcs look good to me except for the very last line, which I don't understand at all. Leave the sin(2t) in your answers - don't try to solve for t.

#### themoleculoma

Oh right, I forgot that :) Still trying to figure out the last part. Thanks

### Want to reply to this thread?

"Induced emf and current"

### Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving