A long, thin, vertical wire has a net positive charge 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.
The particle is later observed to move in a straight line trajectory, parallel to the wire but at a distance 2r
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:
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 2r
, 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
), while it will decrease electric force by 4 (F
^2). So how come the speed is still the same?? I expect it to be u
/2. What did I miss here?