A proton is located at the origin of a rectilinear coordinate system. An electron is at x=4pm, y=3pm. What is the force on the proton. Give your answer in unit vector notation.
You can do this in each direction
Fx= kqq/x^2 fy= kqq/y^2
then the resultant force will be the vector addition of these two.
To calculate the force on the proton due to the electron, we can use Coulomb's law. Coulomb's law states that the force between two charged particles is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.
The formula for Coulomb's law is:
F = (k * q1 * q2) / r^2
where F is the force between the charges, k is the electrostatic constant (9 x 10^9 N m^2/C^2), q1 and q2 are the charges of the two particles, and r is the distance between them.
In this case, the proton and the electron both have charges equal in magnitude but opposite in sign. The charge of a proton is +1.602 x 10^-19 C, and the charge of an electron is -1.602 x 10^-19 C.
The distance between them can be found using the Pythagorean theorem:
r = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Given that the electron is at x = 4 pm and y = 3 pm, and the proton is at the origin (x = 0, y = 0), we can substitute these values into the equation to get:
r = sqrt((4 pm - 0)^2 + (3 pm - 0)^2)
Simplifying further:
r = sqrt(16 pm^2 + 9 pm^2)
r = sqrt(25 pm^2)
r = 5 pm
Now, we can use Coulomb's law to calculate the force:
F = (k * q1 * q2) / r^2
F = (9 x 10^9 N m^2/C^2) * ((1.602 x 10^-19 C)^2) / (5 pm)^2
Calculating this expression will give us the magnitude of the force between the charges. However, we also want the answer in unit vector notation, which means representing the force as a vector with both magnitude and direction.
The direction of the force will be along the line connecting the proton and the electron. Since the electron is at (4 pm, 3 pm) and the proton is at the origin (0, 0), the force vector will point from the origin towards the electron.
Therefore, the unit vector notation for the force on the proton will be:
F = (magnitude of the force) * (unit vector in the direction of the force)
To find the magnitude of the force, we calculate the expression as mentioned above.
Once we have the magnitude, we can find the direction by dividing the vector connecting the proton and electron coordinates by the distance between them. This will give us the unit vector in the direction of the force.
Finally, we can represent the force on the proton in unit vector notation by multiplying the magnitude by the unit vector in the direction of the force.