Question

A proton is at the origin and an electron is at the point x = 0.36 nm , y = 0.39 nm . Find the electric force on the proton.Express your answer using two significant figures. Enter your answers numerically separated by a comma.

Answer 1

The electric force on a proton can be calculated using Coulomb's Law and the charges and distance between the proton and electron. The charge of both particles is ±1.602 × 10^{-19} C, and the distance is calculated from their coordinates on the x and y-axis.

Step-by-step explanation:

To find the electric force on the proton, we can use Coulomb's Law. Coulomb's Law states that the force between two charges is proportional to the product of the charges and inversely proportional to the square of the distance between them.

The formula for Coulomb's Law is:
F = k * |q1 * q2| / r2,

where F is the force, k is Coulomb's constant (approximately 8.9875 × 109 N m2/C2), q1 and q2 are the charges of the particles, and r is the distance between them.

The charge of a proton (q1) and an electron (q2) is approximately ±1.602 × 10−16 C.

The distance r can be found using the Pythagorean theorem, since we have the x and y coordinates:

r = √(x2 + y2) = √(0.362 + 0.392).

After calculating the distance r, we can plug all the values into the Coulomb's Law formula to get the magnitude of the force.

Answer 2

The electric force on the proton is 8.2x10^-10 N

Step-by-step explanation:

We use the formula to calculate the distance between two points, as follows:

r = ((x2-x1)^2 + (y2-y1)^2)^1/2, where x1 and x2 are the x coordinate, y2, y1 are the y coordinate. replacing values:

r = ((0.36-0)^2 + (0.39-0)^2)^1/2 = 0.53 nm = 5.3x10^-10 m

We will use the following expression to calculate the electrostatic force:

F = (q1*q2)/(4*pi*eo*r^2)

Here we have:

q1 = q2 = 1.6x10^-19 C, 1/4*pi*eo = 9x10^9 Nm^2C^-2

Replacing values:

F = (1.6x10^-19*1.6x10^-9*9x10^9)/((5.3x10^-10)^2) = 8.2x10^-10 N