Awire is oriented along the x-axis. it is connected to two batteries, and a conventional current of 2.4 a runs through the wire, in the +x direction. along 0.27 m of the length of the wire there is a magnetic field of 0.62 tesla in the +y direction, due to a large magnet nearby. at other locations in the circuit, the magnetic field due to external sources is negligible. what is the magnitude of the magnetic force on the wire?

Explanation:

To calculate the force we need to use this equation

where L is the total length of the wire

So in this case the small element of current is

Because x is the direction of the current flow.

As is said in the problem B is such that

so to use the equation above we first calculate the following cross product:

so the force:

So here we use the fact that B=0 in any point of the x axis that is not , that means that we only need to do the integration between a very short distant behind the point and a very short distant after that point, meaning:

so is the same as evaluating at

that is:

we have been given a quadratic function and we need to restrict the domain such that it becomes a one to one function.

we know that vertex of this quadratic function occurs at (5,2).

further, we know that range of this function is .

if we restrict the domain of this function to either or , it will become one to one function.

let us know find its inverse.

upon interchanging x and y, we get:

let us now solve this function for y.

hence, the inverse function would be if we restrict the domain of original function to and the inverse function would be if we restrict the domain to .