4. As shown in the figure shown below, find the total electric potential due to the two point charges A and B.
+8.0 x 10-9 C A B -8.0 x 10-9 C
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0.20 m 0.20 m 0.40 m
To find the total electric potential due to the two point charges A and B, we can use the formula for electric potential:
V = k * (q1/r1 + q2/r2)
where V is the electric potential, k is the Coulomb constant (approximately equal to 9 x 10^9 Nm^2/C^2), q1 and q2 are the charges, and r1 and r2 are the distances between the charges and the point where we want to find the potential.
In this case, charge A has a magnitude of +8.0 x 10^-9 C, and charge B has a magnitude of -8.0 x 10^-9 C. Both charges are located at a distance of 0.20 m from the point where we want to find the potential.
Using the formula, we can calculate the potential due to each charge individually:
V_A = k * (q1/r1) = (9 x 10^9 Nm^2/C^2) * (8.0 x 10^-9 C / 0.20 m)
V_A = 36 x 10^9 Nm/C
V_B = k * (q2/r2) = (9 x 10^9 Nm^2/C^2) * (-8.0 x 10^-9 C / 0.20 m)
V_B = -36 x 10^9 Nm/C
Note that the negative sign indicates the opposite sign of the charge.
To find the total potential, we just need to add the potentials due to each charge:
V_total = V_A + V_B
V_total = (36 x 10^9 Nm/C) + (-36 x 10^9 Nm/C)
V_total = 0 Nm/C
Therefore, the total electric potential due to the two point charges A and B is zero.
To find the total electric potential due to the two point charges A and B, we need to calculate the electric potential due to each charge individually and then add them together.
1. Electric potential due to charge A:
- The charge of point charge A is +8.0 x 10^-9 C (Coulombs).
- The distance between point charge A and the point where we want to find the electric potential is 0.20 m.
- The formula to calculate the electric potential due to a point charge is V = k * q / r, where V is the electric potential, k is the Coulomb's constant (k = 9 x 10^9 N m^2 / C^2), q is the charge, and r is the distance.
- Plugging in the values, we get V_A = (9 x 10^9 N m^2 / C^2) * (8.0 x 10^-9 C) / (0.20 m).
2. Electric potential due to charge B:
- The charge of point charge B is -8.0 x 10^-9 C (Coulombs).
- The distance between point charge B and the point where we want to find the electric potential is 0.40 m.
- Using the same formula as above, we get V_B = (9 x 10^9 N m^2 / C^2) * (-8.0 x 10^-9 C) / (0.40 m).
3. Total electric potential:
- To find the total electric potential, we add the electric potentials due to point charges A and B together: V_total = V_A + V_B.
Now, you can substitute the given values into the equations and calculate the individual potentials due to charges A and B, and their sum to find the total electric potential.