*L*per unit length. In addition, there is a current

*I*in the wire. A charged particle moves with speed

*u*in a straight line trajectory, parallel to the wire and at a distance

*r*from the wire. Assume that the only forces on the particle are those that result from the charge on and the current in the wire and that

*u*is much less than

*c*, the speed of light.

Q:

The particle is later observed to move in a straight line trajectory, parallel to the wire but at a distance 2

*r*from the wire. If the wire carries a current

*I*and the charge per unit length is still

*L*, the speed of the particle is:

A) 4

*u*

B) 2

*u*

C)

*u*

D)

*u*/2

E)

*u*/4

Correct answer is (C).

Actually this is related to previous problem (Q28) in which the current was reduced to

*I*/2, then doubling the speed of the particle is necessary to keep it in the same trajectory at distance

*r*. So in this problem the magnetic force is towards the wire direction and electric force is away from the wire -- if both forces are of the same strength then the particle will keep moving straight.

What I don't understand is why it is still moving at speed

*u*at distance 2

*r*, while the other parameters are still the same value. The factor 2 increase of distance to the wire will decrease magnetic force by 2 (

*B*~ 1/

*r*), while it will decrease electric force by 4 (

*F*~ 1/

*r*^2). So how come the speed is still the same?? I expect it to be

*u*/2. What did I miss here?