# Why do I have to use integration and components?

in the picture.

## Homework Equations

F=ILcrossB
Along with the original question, the other picture contains the solution with different numbers. I was just wondering why when finding the force on the wire instead of making dl= R*dtheta and going through the integration and separating the force into to components. Why isn't it possible to simply solve the equation for F=ILBsin90 with L= 2*pi*r/4?

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in the picture.
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in the picture.

## Homework Equations

F=ILcrossB
Along with the original question, the other picture contains the solution with different numbers. I was just wondering why when finding the force on the wire instead of making dl= R*dtheta and going through the integration and separating the force into to components. Why isn't it possible to simply solve the equation for F=ILBsin90 with L= 2*pi*r/4?
From what you've learned (using the right-hand rule), what is the direction of the differential force on each small section of the wire?

haruspex