Questions and Answers
Calculate the net force on the 1 Coulomb charge at position 6 due to the -5 Coulomb charge at position 2 and the 3 Coulomb charge at position 4. Include the direction of the net force.
The net force is 16 N directed to the left (toward position 2).
What is the force exerted on the 1 Coulomb charge at position 6 by the -5 Coulomb charge at position 2?
The force is 10 N directed to the left.
What is the force exerted on the 1 Coulomb charge at position 6 by the 3 Coulomb charge at position 4?
The force is 4.5 N directed to the right.
Describe how the positions of the charges affect the net force on the 1 Coulomb charge at position 6.
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Explain how Coulomb's law is used to determine the net force on the 1 Coulomb charge at position 6.
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Study Notes
Charge Configuration
- A -5 Coulomb charge is located at position 2 on the x-axis.
- A 3 Coulomb charge is positioned at 4 on the x-axis.
- A 1 Coulomb charge is situated at position 6 on the x-axis.
Forces Calculation
- The force between two charges can be calculated using Coulomb's Law: ( F = k \frac{|q_1 \cdot q_2|}{r^2} ), where ( k ) is Coulomb's constant.
- The distance between the -5 Coulomb charge at position 2 and the 1 Coulomb charge at position 6 is 4 units.
- The distance between the 3 Coulomb charge at position 4 and the 1 Coulomb charge at position 6 is 2 units.
Force from -5 Coulomb Charge
- The force exerted by the -5 Coulomb charge on the 1 Coulomb charge is attractive due to opposite charges.
- The magnitude of the force can be calculated as follows:
- ( F_{1} = k \frac{|-5| \cdot |1|}{4^2} = k \frac{5}{16} ).
Force from 3 Coulomb Charge
- The force exerted by the 3 Coulomb charge on the 1 Coulomb charge is repulsive due to the same type of charge.
- The magnitude of the force can be calculated as follows:
- ( F_{2} = k \frac{|3| \cdot |1|}{2^2} = k \frac{3}{4} ).
Net Force on the 1 Coulomb Charge
- The net force on the 1 Coulomb charge at position 6 is the vector sum of forces from the other two charges.
- Since the force from the -5 Coulomb charge is attractive (to the left) and the force from the 3 Coulomb charge is repulsive (to the right), the net force can be determined by subtracting ( F_{1} ) from ( F_{2} ).
Direction of Net Force
- The direction of the net force on the 1 Coulomb charge is determined by the comparison of magnitudes:
- If ( F_{1} < F_{2} ), the net force will be to the right.
Conclusion
- The exact values of ( F_{1} ) and ( F_{2} ) will help to establish the overall direction of the force acting on the 1 Coulomb charge at position 6.
- The force's overall impact is governed by the relative distances and magnitudes of the charges involved.
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Description
This quiz tests your understanding of electrostatics by asking you to calculate the net force on a charge due to other charges placed on the x-axis. You will encounter various scenarios involving different charge magnitudes and positions, requiring you to determine both the magnitude and direction of the resultant force.
