A +50 micro coulomb and 30 micro coulomb charge are placed 50cm apart.

a)what is the direction and magnitude of thee electric field at a point P, in between them, that is 10cm from the 30 micro coulomb charge?

b)if an electron is placed at rest P, what will its acceleration be initially?

c)at what points along the line joining them is the electric field zero?

d)at what points along the line joining them is the potential zero?

To answer the given questions, we will need to use the principles of electrostatics and Coulomb's law. Let's break down each question and explain how to arrive at the answer.

a) To find the electric field at point P, we can use Coulomb's law, which states that the electric field produced by a point charge is directly proportional to the magnitude of the charge and inversely proportional to the square of the distance from the charge.

The formula for electric field (E) is:
E = k * (Q / r^2)

Where Q is the charge, r is the distance from the charge, and k is Coulomb's constant.

In this case, we have two charges: +50 μCoulomb and +30 μCoulomb. Let's assume the 50 μCoulomb charge is at point A, and the 30 μCoulomb charge is at point B. Point P is located 10 cm from the 30 μCoulomb charge.

First, calculate the electric field produced by the +50 μCoulomb charge at point P:
E1 = k * (Q1 / r1^2)

Then, calculate the electric field produced by the +30 μCoulomb charge at point P:
E2 = k * (Q2 / r2^2)

Finally, find the net electric field by adding the two electric fields together:
E_net = E1 + E2

Make sure to include the direction (which can be positive or negative) and magnitude of the electric field.

b) To find the initial acceleration of an electron placed at rest at point P, we can use Newton's second law of motion. The force experienced by the electron is given by the equation: F = m * a, where m is the mass of the electron and a is its acceleration.

The force experienced by the electron is the Coulomb force exerted on it due to the presence of the charges at points A and B. The equation for the force is: F = q * E, where q is the charge of the electron, and E is the electric field at point P.

Using the known value of charge and the calculated electric field at point P, we can determine the force on the electron. Dividing this force by the mass of an electron will give us the initial acceleration of the electron.

c) To determine the points along the line joining points A and B where the electric field is zero, we need to find the positions where the electric field produced by the +50 μCoulomb charge is equal to the electric field produced by the +30 μCoulomb charge. This means that the two electric fields should cancel each other out.

By setting E1 = E2, and solving for the distance from the +50 μCoulomb charge, we can find the locations where the electric field is zero.

d) To find the points along the line joining points A and B where the potential is zero, we need to determine the positions where the sum of the potential due to the +50 μCoulomb charge and the potential due to the +30 μCoulomb charge is equal to zero. The potential at a point due to a charge is given by V = k * (Q / r), where Q is the charge and r is the distance from the charge.

By setting the potential due to the +50 μCoulomb charge at a point equal to the negative potential due to the +30 μCoulomb charge at the same point, and solving for the distance from the +50 μCoulomb charge, we can find the locations where the potential is zero.

Remember to use the appropriate units and conversion factors in all calculations.