Two charges of # 6 C # and # -7 C# are positioned on a line at points # -7 # and # 8 #, respectively. What is the net force on a charge of # 6 C# at # 2 #?

Question

Two charges of #  6  C # and #  -7   C# are positioned on a line at points # -7  # and # 8  #, respectively.  What is the net force on a charge of #  6  C# at #  2  #?

William Audy · Accepted Answer

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Adam Arnold · Answer

undefined To calculate the net force on a charge of 6 C at position 2, we need to consider the forces exerted by each charge using Coulomb's law. Coulomb's law states that the force between two charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them.

Given:
- Charge 1: 6 C
- Charge 2: -7 C
- Positions: Charge 1 at -7 and Charge 2 at 8
- Position of interest: 2

First, we need to find the distances between the charge of 6 C and each of the other charges:
- Distance from the charge of 6 C to the charge at -7: $|2 - (-7)| = 9$
- Distance from the charge of 6 C to the charge at 8: $|2 - 8| = 6$

Now, we can calculate the magnitudes of the forces exerted by each charge on the charge of 6 C using Coulomb's law:
- Force exerted by the charge at -7: $F_1 = \frac{k \cdot |6 \, \text{C}| \cdot |-7 \, \text{C}|}{9^2}$
- Force exerted by the charge at 8: $F_2 = \frac{k \cdot |6 \, \text{C}| \cdot |-7 \, \text{C}|}{6^2}$

Where $k$ is Coulomb's constant, approximately $8.99 \times 10^9 \, \text{N} \cdot \text{m}^2/\text{C}^2$.

After calculating $F_1$ and $F_2$, we determine their directions based on the sign of the charges:
- The force from the charge at -7 is repulsive since it has the same sign as the charge of 6 C.
- The force from the charge at 8 is attractive since it has the opposite sign.

Finally, we find the net force by adding the forces vectorially, considering their directions. The net force is the vector sum of the individual forces. If both forces have the same direction, we add them. If they have opposite directions, we subtract the smaller force from the larger one.

Therefore, to find the net force on the charge of 6 C at position 2, we calculate the magnitudes of the forces exerted by each charge and determine their directions, then sum or subtract accordingly to find the resultant force.