Consider a straight wire that has a mass per length of 100 g

Consider a straight wire that has a mass per length of 100 g/m, a fixed charge per unit length of ?35 ?C/m, and a current can run from left to right as shown on the attached figure. A uniform electric field of 12000 N/C exists that is directed straight up, and there is a uniform B field of magnitude 0.04 T that is free to point in any direction.

Solution

a)

For equilibrium,

net force = 0

forces acting on the wire :

1) force of gravity = mg <--- acting downwards

2) magnetic force = BIL <--- must act in a direction such that net force = 0

3) electric force = Q*E <------ acting downwards

So, BIL = mg - EQ

So, 0.4*I = (m/L)*g + E*(Q/L)

So, 0.4*I = (0.1)*9.8 + 12000*35*10^-6

So, I = 3.5 A <--------- current needed (ANSWER)

Now, for magnetic force to be directed in the upwards direction, the magnetic field must be directed into the page

So, answer is into the page <----------answer(for magnetic field )