- #1

- 20

- 0

## Homework Statement

Given: a quarter-circle of wire (radius r=0.75m) in a uniform 1.7T magnetic field carrying a current of 3.5A (see diagram)

Find: The force on the wire.

Note: the connecting wires delivering the current to the quarter circle are parallel to the magnetic field and experience no force.

## Homework Equations

d

**F**= I d

**S**x

**B**

## The Attempt at a Solution

I know of two ways to solve this.

The first is to use the fact that the force is path-independent and use the

**F**= I

**L**x

**B**formulation; we're not supposed to do that, as this is supposed to be a calculus problem.

The second is the way my instructor suggested to the class, which is to argue by symmetry that the force is directed at a 45 degree angle outward from the origin. I can then treat it like a scalar integration problem and use the fact that the magnitude of d

**S**is r d(theta). It's really a quite simple problem this way, but it only works because the problem is particularly simple.

Having done vector calculus, I feel like there

*ought*to be a third way to attack the thing; it should be possible to parameterize the curve and do something like a line integral. The advantage would be that the same approach would work for a messier problem, where e.g. the magnetic field was nonuniform so the direction wasn't plainly obvious. But I'm not quite sure where to begin. I've got the following parameterization:

x(t) = r sin t

y(t) = r cos t

z(t)=0

0 <= t <= pi/2

but I'm not sure where to go from there. Any ideas?