Question

A -4.00 nC point charge is at the origin, and a second -6.00 nC point charge is on the x-axis at x = 0.800 m. Find the net electric force that the two charges would exert on an electron placed at point on the x -axis at x = 0.200 m'

Answer 1

The net electric force that the two charges would exert on an electron placed at point on the x -axis is 1.68 x 10⁻¹⁶ N.

Force on electron due to charge 1

The force exerted on the electron due to the charge q1 placed at the origin is calculated as follows;

F = kq₀q₁/r²

where;

• k is coulomb's constant
• q0 is charge at the origin
• q1 is the charge at 0.2 m (electron)
• r is the distance between the charges

F(01) = (9 x 10⁹ x 4 x 10⁻⁹ x 1.6 x 10⁻¹⁹)/(0.2²)

F(01) = 1.44 x 10⁻¹⁶ N

Force on electron due to charge 2

The force exerted on the electron due to the charge q1 placed at the origin is calculated as follows;

F = kq1q2/r²

where;

• k is coulomb's constant
• q2 is charge at the 0.8 m
• q1 is the charge at 0.2 m (electron)
• r is the distance between the charges = 0.8 m - 0.2 m = 0.6 m

F(12) = (9 x 10⁹ x 6 x 10⁻⁹ x 1.6 x 10⁻¹⁹)/(0.6²)

F(12) = 2.4 x 10⁻¹⁷ N

Net force on the electron

F(net) = 2.4 x 10⁻¹⁷ N +  1.44 x 10⁻¹⁶ N

F(net) = 1.68 x 10⁻¹⁶ N

Thus, the net electric force that the two charges would exert on an electron placed at point on the x -axis is 1.68 x 10⁻¹⁶ N.

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