Two charged particles of equal magnitude (+Q and −Q) are fixed at opposite corners of a square that lies in a plane (see figure below). A test charge +q is placed at a third corner.
+Q
+q −Q What is the direction of the force on the
test charge due to the two other charges?
To determine the direction of the force on the test charge (+q) due to the two other charges (+Q and -Q), we need to apply 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.
Here are the steps to find the direction of the force:
1. Identify the magnitudes of the charges:
- The fixed charges at the corners are +Q and -Q.
- The test charge at the third corner is +q.
2. Determine the direction from the positive charge (+Q) to the test charge (+q) and the negative charge (-Q) to the test charge (+q).
3. Apply Coulomb's Law:
- The force on the test charge (+q) due to +Q will be attractive, pulling the test charge towards +Q.
- The force on the test charge (+q) due to -Q will be repulsive, pushing the test charge away from -Q.
In conclusion, the force on the test charge due to the two other charges will be in opposite directions. The force from the positive charge (+Q) will be attractive, pulling the test charge towards it, and the force from the negative charge (-Q) will be repulsive, pushing the test charge away.
To determine the direction of the force on the test charge, we need to consider the principles of electrostatics.
1. The force between two charges is directly proportional to the magnitude of the charges and inversely proportional to the square of the distance between them, as given by Coulomb's Law.
2. The direction of the force is along the line connecting the charges and acts repulsively between like charges (same sign) and attractively between opposite charges.
In this case, we have two charges: +Q and -Q, fixed at opposite corners of a square, and a test charge +q placed at a third corner.
Since the charges +Q and -Q have opposite signs, they will attract each other. Therefore, the force between them will act along the diagonal of the square, from the positive charge (+Q) to the negative charge (-Q).
Similarly, the test charge +q will experience a force from each of the fixed charges (+Q and -Q). Since the test charge has the same sign as the positive charge (+Q), the force between them will be repulsive. Hence, the force on the test charge due to the fixed charges will act away from the positive charge (+Q) and towards the negative charge (-Q).
So, the direction of the force on the test charge (+q) due to the two other charges (+Q and -Q) is from the positive charge (+Q) towards the negative charge (-Q), along the diagonal of the square.
Note: The actual magnitude of the force will depend on the specific values of the charges involved and the distance between them. The given information does not provide enough details to calculate these values.