Emf long straight wire & loop

[sona1177]

Homework Statement

A square loop of wire of side 2.8 cm and electrical resistance 79 ohms is near a long straight wire that carries a current of 6.9 A North. The long wire and loop both lie in the plane of the screen. THe left side of the loop is 9.0 cm from the wire. Find the motional emf if the loop is moving to the right at 55 cm/s.

For both the right and left wire, the magnetic field points into the page, and I know i need the net magnetic field to solve for the E=vBL

Do I just add the magnetic fields due to each wire since they point in the same direction?

Homework Equations

The Attempt at a Solution

Homework Statement

Homework Equations

The Attempt at a Solution

 

[jbsteele]

Yes, you can add the magnetic fields due to each wire since they point in the same direction. The magnetic field due to the long wire is given by B = (μ0I)/(2πr) where μ0 is the permeability of free space, I is the current, and r is the distance from the wire. For the left side of the loop, the distance is 9.0 cm so the magnetic field due to the wire is B = (μ0*6.9 A)/(2π*0.09 m) = 3.48 T. For the right side of the loop, the distance is 2.8 cm so the magnetic field due to the wire is B = (μ0*6.9 A)/(2π*0.028 m) = 11.5 T. The net magnetic field is then (3.48 + 11.5) T = 14.98 T. The motional emf is then given by E = vBL = (55 cm/s)*(14.98 T)*(2.8 cm) = 101.4 V.