A particle with a mass of 1 mg and a charge q is seen to travel with a speed of 1000 m/s parallel to a straight current carrying wire along a horizontal path 10 cm below the wire as shown in the figure.Determine q if the magnitude of current in the wire is 10 A.
A)1.0 C
B)0.49 C
C)0.24 C
D)2.0 C

Question

A particle with a mass of 1 mg and a charge q is seen to travel with a speed of 1000 m/s parallel to a straight current carrying wire along a horizontal path 10 cm below the wire as shown in the figure.Determine q if the magnitude of current in the wire is 10 A. 
A)1.0 C 
B)0.49 C 
C)0.24 C 
D)2.0 C

Quizplus · Accepted Answer

The force on a charged particle moving with velocity v, in a magnetic field of intensity B, is given by the formula F=qvB. 
In this problem, the wire carrying current produces a magnetic field B at the location of the particle, which is moving parallel to the wire. The force on the particle is thus perpendicular to its velocity and the wire, and points towards the wire. 
Using the given distance of 10 cm and applying the right-hand rule, we can determine that the magnetic field produced by the current-carrying wire has a magnitude of 2 x 10^-5 T at the location of the particle. 
The force on the particle is then F = qvB = m*a, where m is the mass of the particle, a is its acceleration, and v and B are as given above. Solving for q gives q = m*a/(v*B) = (1x10^-6 kg)(9.81 m/s^2)/(1000 m/s)(2x10^-5 T) = 0.49 C. 
Therefore, the answer is B.

A Particle with a Mass of 1 Mg and a Charge