Calculating Electromagnetic Force on a Moving Wire

[FerN61]

Homework Statement

A wire of length L=20cm travels with an acceleration a=0.002m/s² perpendicular to the Earth's magnetic field (B=20μT). Considering that the wire starts from rest, calculate the value of the emf (electromagnetic force) when an hour has gone by.

Homework Equations

My question: Is current being induced in the wire by the magnetic field?

The Attempt at a Solution

I know I first need to calculate a magnetic flux.

So I got the speed after one hour:

V=Vo+at = 0+3600(.002) = 7.2 m/s

Then, magnetic fied for a finite wire:

B=(μ0 I /4 pi r) 2*∫cos (opposite angle) from 0 to pi/4

20μT= (√2 μ0 I )/ 4 pi r

141.42 = I / r = (dq/dt) / r

I'm thinking since the magnetic field is perpendicular, there is a centripetal acceleration and I can get the radius from there, but I got stuck, and I'm not even sure if the previous work is right. I don't really know how tho get the magnetic flux if the wire is moving, and I thought an area was needed, but this is just a wire. Any help will be greatly appreciated. Thank you.

 

[rude man]

Homework Statement

A wire of length L=20cm travels with an acceleration a=0.002m/s² perpendicular to the Earth's magnetic field (B=20μT). Considering that the wire starts from rest, calculate the value of the emf (electromagnetic force) when an hour has gone by.

Homework Equations

My question: Is current being induced in the wire by the magnetic field?

In a sense, yes. Since the wire is accelerating, a continuous buildup of charge occurs at both ends of the wire. But it has nothing to do with answering the question. For this question the answer is No.

The Attempt at a Solution

I know I first need to calculate a magnetic flux.

So I got the speed after one hour:

V=Vo+at = 0+3600(.002) = 7.2 m/s

Then, magnetic fied for a finite wire:

B=(μ0 I /4 pi r) 2*∫cos (opposite angle) from 0 to pi/4

Whoa. There is no steady-state current in the wire. This formula is totally inappropriate here. We are not looking at a B field set up by the wire. The B field is set up by the Earth.

You have an open wire with no current, far as you're concerned. What is the expression for induced emf in a wire of length L when it's moving perpendicularly to the B field with a velocity perpendicular to B and L?