Four electrons are located at the corners of a square 10.0 nm on a side, with an alpha particle at its midpoint. Part A How much work is needed to move the alpha particle to the midpoint of one of the sides of the square?

Explanation:

The work done on alpha is given by

Charge on alpha particle is 2 the electron charge

The potential at center

The electric potential due to multiples point charges is given by

where =charge on electron

=charge on alpha particle

But  and is equal for all charges so ( 2) is equal to

The radius  is given by

Substitution in (3) yields

The potential at mid point

due to lower charges the radius  is given by

And for upper charges the radius is

So the electric potential is

The work done on the charge is equal to

The work done on  is given by

The potential at center

The electric potential due to multiples point charges is given by

But  and is equal for all charges so ( 2) is equal to

The radius  is given by

Substitution in (3) yields

The potential at mid point

due to lower charges the radius  is given by

And for upper charges the radius is

So the electric potential is

The work done on the charge is equal to

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