Question

If two electrons are each 1.5 x 10-10 m from a proton, as shown in Figure, magnitude of the net electric force they will exert on the proton is

65.0°​

Answer 1

Explanation:

$f = q {}^{2} \div {r}^{2} \\ the \: total \: force \: will \: be \: \\ 2 \times f \\ or \\ 2 {q }^{2} \div r { }^{2}$

Answer 2

Given:

Distance between electron and proton = 1.5 X 10⁻¹⁰m

Number of electrons = 2

To find:

The magnitude of the net electric force on the proton

Solution:

According to Coulomb's law of electrostatics, Electric Force F = k q1 q1 / r²

Here, k = 9 X 10⁹ kg⋅m³⋅s⁻²⋅C⁻² and r is the distance between the charges.

F due to each electron  = 9 X 10⁹ X 1.6 X 10⁻¹⁹ X 1.6 X 10⁻¹⁹ / (1.5 X 10⁻¹⁰ )²

Since force is a vector quantity, the net magnitude of the force on the proton is calculated using the vector formula = $\sqrt{F^2 + F^2 + 2 F.F cos 65}$

Taking cos 65 =0.42,

Net force = 1.97 X 10⁻⁸N

Hence the magnitude of the net electric force on the proton is 1.97 X 10⁻⁸N.

The direction of the individual forces on the proton is towards the electrons. The net force is shown in the figure attached below.