A charge of +24.3 µC is located at (4.40 m, 6.02 m) , and a charge of -13.1 µC is located at (-4.50 m, 6.75 m) . What charge must be located at (2.23 m, -3.01 m) if the electric potential is to be zero at the origin?
ANyone have any advice?
Find the distances to the center.
Potential is a scalar.
0= V1 + V2 + V3
where V1= k q1/r1 ; V2= kq2/r2 ; and V2= kq3/r3
solve for q3
To find the charge that must be located at (2.23 m, -3.01 m) for the electric potential to be zero at the origin, we can follow these steps:
1. Calculate the distances from each charge to the origin using the distance formula: d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
For the given charges:
- Distance from the charge of +24.3 µC at (4.40 m, 6.02 m) to the origin is d1 = sqrt((0 - 4.40)^2 + (0 - 6.02)^2)
- Distance from the charge of -13.1 µC at (-4.50 m, 6.75 m) to the origin is d2 = sqrt((0 - (-4.50))^2 + (0 - 6.75)^2)
2. Calculate the electric potentials (V) for each charge using the formula: V = (k * q) / r, where k is the electrostatic constant (8.99 x 10^9 Nm^2/C^2), q is the charge, and r is the distance.
For the given charges:
- Electric potential V1 for the charge of +24.3 µC is V1 = (8.99 x 10^9 Nm^2/C^2) * (24.3 x 10^-6 C) / d1
- Electric potential V2 for the charge of -13.1 µC is V2 = (8.99 x 10^9 Nm^2/C^2) * (-13.1 x 10^-6 C) / d2
3. Since the electric potential at the origin is zero (V = 0), we can write the equation:
0 = V1 + V2 + V3, where V3 is the potential at the point (2.23 m, -3.01 m) for an unknown charge q3.
4. Rearrange the equation to solve for q3:
q3 = -V1 - V2
5. Substitute the values of V1 and V2 and solve:
q3 = -[(8.99 x 10^9 Nm^2/C^2) * (24.3 x 10^-6 C) / d1] - [(8.99 x 10^9 Nm^2/C^2) * (-13.1 x 10^-6 C) / d2]
By evaluating this expression using the calculated values of d1 and d2, you can find the charge (q3) that must be located at (2.23 m, -3.01 m) for the electric potential to be zero at the origin.