In the rectangle in the drawing, a charge is to be placed at the empty corner to make the net force on the charge at corner a point along the vertical direction. what charge (magnitude and algebraic sign) must be placed at the empty corner?

Charge,

Explanation:

The added charge must create the force which is both equal and opposite to the charge that is caused by 3μC in the lower right corner.

Now we know that the electrostatic force of a charge is given by

We know

Electrostatic force between the charges at the corner is

Then to find the charge, q' we get F=F'

=

Now substituting q = 3μC. we get

The charge that must be placed at the empty corner is : q' = -3.29 * 10⁻⁶ C

Given that the Electrostatic force of a charge is expressed as

F = ---- ( 1 )

The added charge ( q' ) will create a charge equal and opposite to the charge ( q ) caused by 3μC

∴ The electrostatic force between the charges at the corner is :

F' =    ----- ( 2 )

Final step : The charge that must be placed at the empty corner ( q' )

where F = F'

Equating  equations ( 1 ) and  ( 2 )

  ------ ( 3 )

Insert  q = 3μC in equation ( 3 )

q' = -3.29 * 10⁻⁶ C

Hence we can conclude that the charge that must be placed at the empty corner is : q' = -3.29 * 10⁻⁶ C

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