In: Physics
What is the line charge density on a long wire if a 7.1-μg particle carrying 1.6 nC describes a circular orbit about the wire with speed 300 m/s?
Express your answer in microcoulombs per meter.
The electric field due to a line charge at a distance r is given
by
And so, the force on a charge q circulating the line charge at the
distance r is given by
And for the circular motion we equate this with the centripetal
force required for the circular motion
where, m is the mass of the charged particle.
And so, simplifying this, we get
Now putting the given values,
we get the line charge density as
We want to mention that the line charge density and the charge of
the particle should be of opposite sign. So, if the rotating
particle has positive sign, then the line charge density should be
negative.