Two long, parallel wires are separated by 2.2 m . Each wire has a 30-A current, but the currents are in opposite directions.

a) Determine the magnitude of the net magnetic field midway between the wires. Express your answer to two significant figures and include the appropriate units.
b) Determine the magnitude of the net magnetic field at a point 1.1 m to the side of one wire and 3.3 mfrom the other wire. The point is in the same plane as the wires. Express your answer to two significant figures and include the appropriate units.

a)10.9 mT

b)3.63 mT

Explanation:

Magnetic field B is equal Current* vacuum permeability /2* pi* R . r being how far the point is away from the current carrying wire.

We also have to consider the right hand loop rule to determine the direction of the magnetic field. Picture two wires with one having current upward and one having current downward being placed side by side. You put your thumb in the direction of the current and wrap your fingers around. the way your fingers curl is the magnetic field. the wire with current going down will have a magnetic field into the page on the left and out of the page on the right.  The wire with current going up will have the opposite. Therefore in between the two wires the magnetic field is going the same direction. and on the side away from the other wire they are going opposite directions.

a) The point midway between the wires 1.1m distance from both of them so this is the r value. since both wires have the same current and radius we just need to do the calculation once and multiply by 2 since magnetic field are in the same direction. we get the magnetic field of one to be 5.45mT therefore the total magnetic field at this point is 10.9mT

b) Since we know these two magnetic fields from the wire are in opposite directions we must subtract the two values. we know at 1.1 m away the magnetic field induced is 5.45mT now we plug in to find the magnetic field at 3.3 m away to be 1.82mT. Now we just subtract to get a magnitude of 3.63mT.

Hope this helps

where are the vectors ?