Question

Problem 4: Three protons are on three corners of a square of side d = 7.8 × 10-6 m.

What will be the magnitude of the net force on an electron put on the fourth corner of the square? Give your answer in newtons.
Useful Information:
Charge of electron = -1.6 × 10-19 C
Charge of proton = 1.6 × 10-19 C
1/(4πε0) = 9 × 109 Nm2 C-2
F = |

Answer 1

To find the net force on the electron, calculate the forces between the electron and each of the adjacent protons and the diagonally opposite proton using Coulomb's law, and then use vector addition to determine the net force magnitude.

Step-by-step explanation:

Given that three protons are on three corners of a square of side d = 7.8 × 10-6 m, and we are tasked to find the magnitude of the net force on an electron put on the fourth corner of the square. The Coulomb's law formula is F = k × |q1 × q2| / r2, where k is the Coulomb's constant (k = 9 × 109 Nm2 C-2), q1 and q2 are charges, and r is the distance between charges.

The net force on the electron is the vector sum of the forces due to each proton. Since the situation is symmetrical, the forces due to the protons on adjacent corners will partially cancel out in the horizontal direction, leaving a net vertical component. The force due to the proton on the diagonally opposite corner will contribute fully to the net force.

We calculate the force between the electron and one of the adjacent protons (or electron-proton force): Fep = (9 × 109 Nm2 C-2) × ((1.6 × 10-19 C)2 / (7.8 × 10-6 m)2). The force between the electron and the diagonally opposite proton (with √d distance) can be similarly calculated.

Finally, using vector addition, we find the net force magnitude (Fnet) on the electron.