Help with problem solving steps to these questions would be greatly appreciated.

Question

Help with problem solving steps to these questions would be greatly appreciated. Can someone explain how you determine that it is into the page with right hand rule? Is the force exerted on the wire always constant or are there fluctuations in some cases?

2. A long straight wire carries a current of 13 A into the page. The wire is located in a region of space where the Earth's B-field is a uniform 7.0 x 10^-5 T directed toward the bottom of the page. a. If the wire is 3.0 m long, find the magnitude and direction of the total magnetic force that the Earth's field exerts on the length of wire. Show your work. Assume that the wire is fixed in position, so that it cannot move. Point P is located 5.0 cm away from the wire, directly toward the bottom of the page, as shown. b. Including both the wire's and the Earth's magnetic fields, find the magnitude and direction of the total (net) magnetic field at point P. (Since 3.0 m > > 5.0 cm, you may assume for this part that the wire is infinitely long.) Show your work completely.

Explanation / Answer

a)

Here , magnetic force acting on the wire is

Fm = BIL

Fm = 13 * 7*10^-5 * 3

Fm = 2.73 *10^-3 N

the magnetic force acting on the wire is 2.73 *10^-3 N

b)

Due to the wire ,

field at P is Fw = u0*I/(2*pi*d) to the left

Fw = u0*13/(2*pi*./0.05)

Fw = 5.2 *10^-5 T

Now, the resultant field at point P

Fp = sqrt((5.2 *10^-5)^2 + (7*10^-5)^2)

Fp = 8.721 *10^-5 T

the resultant magnetic field at point P is 8.721 *10^-5 T

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