A magnetic field has a magnitude and an electric field has a magnitude both fields point in the same direction determine the magnitude of the net force that acts on the charge?

Answer 1

There are a few possibilities. First, if the charge q is at rest in the electric field E and magnetic field B, then only the electric field exerts a force because the charge must be moving for the magnetic field to exert a force. This electrostatic force is qE and its parallel to E if q is positive and antiparallel if q is negative. Second, if the charge is moving with velocity v ,the electric force is same as above. The magnetic force will now be qvBSin(A), Where A is the angle between the directions of B&v. If q is positive the direction of the magnetic force is perpendicular to the plane formed by B & v as found by curling the fingers of your right hand from v toward B. If q is negative its opposite the positive case. Notice; if v is parallel or antiparallel to B then Sin(0) or Sin(180) is zero and the magnetic force is zero. If v is perpendicular to B then Sin(90) =1 and the force is maximum. You always use the smallest angle A between the directions of B & v so it will never be greater then 180 deg. The Net force will then be the vector sum of these two forces. It would be a special case if qE & qvBSin(A) were parallel so you do have to pay attention to the directions when getting the vector sum. In your problem, if the charge is initially at rest then qE will cause it to accelerate parallel to E, which is also parallel to B, so there will never be a magnetic force. If, on the other hand, the charge moves into the fields with some velocity not parallel to the fields then you have to do the full analysis described above.