What are the magnitude and direction of the electric field at a point midway between a -8.0 microCoulomb and a +7.0microCoulomb charge 8.0cm apart? Assume no other charges are nearby.
I have been working on this problem for a few hours now and I haven't really accomplished much on it. Any help will be appreciated!
To find the magnitude and direction of the electric field at a point midway between two charges, you can use Coulomb's law and the principle of superposition.
Coulomb's law states that the electric field created by a point charge is proportional to the magnitude of the charge and inversely proportional to the square of the distance from the charge. It is given by the equation:
E = k * Q / r^2
Where E is the electric field, k is the electrostatic constant (9 x 10^9 Nm^2/C^2), Q is the charge, and r is the distance from the charge.
In this case, we have two charges: -8.0 microCoulomb (Q1) and +7.0 microCoulomb (Q2), located 8.0 cm apart (r).
To find the electric field at the midpoint, we need to calculate the electric fields created by each charge separately and then add them vectorially due to the principle of superposition.
Step 1: Calculate the electric field created by Q1 at the midpoint.
- Calculate the distance from Q1 to the midpoint (r1).
- Use Coulomb's law to find the magnitude of the electric field created by Q1 at the midpoint.
Step 2: Calculate the electric field created by Q2 at the midpoint.
- Calculate the distance from Q2 to the midpoint (r2).
- Use Coulomb's law to find the magnitude of the electric field created by Q2 at the midpoint.
Step 3: Add the electric fields created by Q1 and Q2 to get the net electric field at the midpoint.
- Since the charges are opposite in sign, their electric fields may have opposite directions. Use the direction of the positive charge (Q2) as the reference direction.
Now, let's go through each step in more detail to find the answer to your question.
Step 1: Calculate the electric field created by Q1 at the midpoint.
- The distance from Q1 to the midpoint is half of the total distance between the charges since it's the midpoint.
- Given that the charges are 8.0 cm apart, the distance from Q1 to the midpoint is 4.0 cm or 0.04 m.
- Use Coulomb's law:
E1 = k * Q1 / r1^2
Substituting the values, we get:
E1 = (9 x 10^9 Nm^2/C^2) * (-8.0 x 10^-6 C) / (0.04 m)^2
Calculate E1 to find the magnitude of the electric field created by Q1 at the midpoint.
Step 2: Calculate the electric field created by Q2 at the midpoint.
- Just like in Step 1, the distance from Q2 to the midpoint is also 4.0 cm or 0.04 m.
- Use Coulomb's law:
E2 = k * Q2 / r2^2
Substituting the values, we get:
E2 = (9 x 10^9 Nm^2/C^2) * (7.0 x 10^-6 C) / (0.04 m)^2
Calculate E2 to find the magnitude of the electric field created by Q2 at the midpoint.
Step 3: Add the electric fields created by Q1 and Q2 to get the net electric field at the midpoint.
- Since the charges are opposite in sign, their electric fields may have opposite directions. Use the direction of the positive charge (Q2) as the reference direction.
- Add the magnitudes of E1 and E2 and take into account their directions to find the net electric field at the midpoint.
The magnitude and direction of the electric field at the midpoint can be determined from the result obtained in Step 3.
I hope this explanation helps you solve the problem! Let me know if you need further assistance.