Three Point charges have equal magnitudes, two being positive and one negative. These charges are fixed to the corners of an equilateral triangle. As the drawing shows(a) The charge at any one corner experiences forces from the charges at the other corners. Do the individual forces exerted by the charges have the same or different magnitudes? (b) At which one or more corners does (do) the charge(s) experience a net force that has the greatest magnitude? (c) At which one or more corners does (do) the charge(s) experience a net force that has the smallest magnitude?
B
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A C
To answer these questions, we can use the principles of electrostatics and apply Coulomb's Law. Coulomb's Law states that the force between two point charges is directly proportional to the magnitude of the charges and inversely proportional to the square of the distance between them.
(a) The individual forces exerted by the charges on each other will have the same magnitudes. This is because the magnitudes of the charges are equal, and the distances between them are also equal since they are fixed to the corners of an equilateral triangle. Therefore, the forces exerted on each charge will be equal in magnitude.
(b) To determine where the charge experiences the net force with the greatest magnitude, we need to consider the vector sum of the forces acting on that charge. Let's analyze each corner (A, B, and C) individually:
At corner A:
- The positive charge at corner B will exert a repulsive force on the charge at A.
- The positive charge at corner C will also exert a repulsive force on the charge at A.
- The net force on the charge at A is the vector sum of the forces from corners B and C.
At corner B:
- The negative charge at corner A will exert an attractive force on the charge at B.
- The positive charge at corner C will exert a repulsive force on the charge at B.
- The net force on the charge at B is the vector sum of the forces from corners A and C.
At corner C:
- The negative charge at corner A will exert an attractive force on the charge at C.
- The positive charge at corner B will also exert an attractive force on the charge at C.
- The net force on the charge at C is the vector sum of the forces from corners A and B.
The magnitudes of these net forces will depend on the distances between the charges and the angles of the triangle. Since the distances are all equal, the magnitudes of the forces will be determined by the angles. In an equilateral triangle, all angles are equal. Therefore, the net forces at each corner will have the same magnitude.
(c) Similarly, to determine where the charge experiences the net force with the smallest magnitude, we need to consider the vector sum of the forces acting on that charge. In an equilateral triangle, where all angles are equal, the net forces at each corner will have the same magnitude. So, the charge(s) will experience the smallest net force at any of the corners.
To summarize:
(a) The individual forces exerted by the charges have the same magnitudes.
(b) The charge(s) experience the net force with the greatest magnitude at any corner of the triangle.
(c) The charge(s) experience the net force with the smallest magnitude at any corner of the triangle.