# 10 cm diameter loop in magnetic field

1. Mar 13, 2017

### ikihi

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

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.

2. Relevant equations

Faraday's Law: εinduced= - (ΔΦb/Δt) = - A ⋅ ΔB / Δt
Lenz's Law

3. The attempt at a solution

a)
εinduced= - (ΔΦb/Δt)
εinduced= -0.50 T/sec ⋅ π ⋅ 0.052m2
εinduced= -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.

Last edited: Mar 13, 2017
2. Mar 14, 2017