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# Force on moving charge, charge density free electron density

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The full question is attached and comes in two parts, the first requires me to find the magnetic force acting on a point charge the second asks me to determine the charge density and current density of the current electrons in the wire as well as the residual positive charge in the wire? Please help and show you working.

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#### Solution Preview

A long straight wire carries a current I. The conduction electrons in the wire have drift speed v and the net charge density of the wire is zero. A point charge Q moves at a speed V parallel to and at a constant distance d from the wire as shown in figure 1. The direction of the velocity of the point charge is the same as the electric current in the wire.

y

Q

d

x

I

1)
Using the coordinate axes shown in figure 1, find the magnetic force acting on the point charge due to the electric current.

The magnetic field due to a long thin conductor carrying current I, at a distance d from it is given by

And its direction is given by right hand thumb rule. Here the current is along x direction so keeping the thumb ...

#### Solution Summary

The force on a moving charge due to current carrying wire, free electron density, charge density and free electron density is calculated.

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