What is the line charge density on a long wire if a 7.1-μg particle carrying 1.6...

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.

Expert Solution

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.

genius_generous answered 2 years ago

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