What is the net force exerted by these two charges on a third charge q 3 = 48.5

Question

What is the net force exerted by these two charges on a third charge q3 = 48.5 nC placed between q1 and q2 at x3 = -1.215m ?

Coulomb's law for the magnitude of the force F between two particles with charges Q and Q' separated by a distance d is

|F| = k|Q*Q'|/d^2

where k =8.854 *10^-12 C^2/(N*m^2) . is the permittivity of free space.

Consider two point charges located on the x axis: one charge, q1 = -20.0 nC , is located at x1 = -1.685 ; the second charge, q2 = 34.0 , is at the origin .

What is the net force exerted by these two charges on a third charge q3 = 48.5 nC placed between q1 and q2 at x3 = -1.215m ? Coulomb's law for the magnitude of the force F between two particles with charges Q and Q' separated by a distance d is |F| = k|Q*Q'|/d^2 where k =8.854 *10^-12 C^2/(N*m^2) . is the permittivity of free space. Consider two point charges located on the x axis: one charge, q1 = -20.0 nC , is located at x1 = -1.685 ; the second charge, q2 = 34.0 , is at the origin

Explanation / Answer

k is NOT the permittivity of free space . It is ( nearly ) its reciprocal , the Coulomb Law constant and it is

8.98 . 10^9

Force on q3 from q2 = k q2 . q3 / 1.215 ^2 = 8.98 * 10^9 * 48.5 * 10^9 * 33 * 10^9 / 1.215^2

= 0.968 . 10^5 N directed away from the origin in the x direction

Force on q3 from q1 = 8.98 * 10^9 * 48.5 * 10^9 * 20 * 10^9 / 0.625^2 = 2.22 . 10^5 N

also directed in the negative x direction

So the total force on q3 is 3.29 . 10^5 N at x.

The powers might be different if the distances are not meant to be in metres.

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