10 cm diameter loop in magnetic field

[ikihi]

Homework Statement

The figure shows a 10-cm diameter loop in three different magnetic fields. The loop's resistance is 0.10 Ω. For each case, determine the induced emf, the induced current, and the direction of the current.

Homework Equations

Faraday's Law: ε_induced= - (ΔΦ_b/Δt) = - A ⋅ ΔB / Δt
Lenz's Law

The Attempt at a Solution

a)
ε_induced= - (ΔΦ_b/Δt)
ε_induced= -0.50 T/sec ⋅ π ⋅ 0.05²m²
ε_induced= -3.93 × 10^-3 V

For part A: The flux is increasing, and the external magnetic field is going upward through the loop, so shouldn't the induced magnetic field go in opposite direction (downward) to oppose the external magnetic field? And so therefore shouldn't the induced current be clockwise around the loop according to the right hand rule?

b)
the flux is decreasing and the magnetic field is going into the loop (into the page). So since the flux through the loop is decreasing wouldn't this say that the the induced magnetic field goes in same direction of external magnetic field to try and prevent the decrease; and thus the current goes counter-clockwise?

c) The field does not penetrate the loop so the emf and current are 0.

 

[TJGilb]

Your reasoning and answers are good, except check your right hand rule for b again.

 

[kuruman]

Don't forget to calculate the value of current in each case.