Physics
Geometry
Magnetism

# 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?

###### March 12, 2009 5:01PM

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.

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