A point charge q2 = -0.5 μC is fixed at the origin of a co-ordinate system as shown. Another point charge q1 = 3.5 μC is is initially located at point P, a distance d1 = 8.8 cm from the origin along the x-axis
1) What is ΔPE, the change in potenial energy of charge q1 when it is moved from point P to point R, located a distance d2 = 3.5 cm from the origin along the x-axis as shown?
To calculate the change in potential energy (ΔPE) of charge q1 when it is moved from point P to point R, we need to consider the formula for potential energy:
ΔPE = PE(R) - PE(P)
The potential energy at a specific point due to a point charge can be calculated using the formula:
PE = k * q1 * q2 / r
Where:
- k is Coulomb's constant (9 x 10^9 Nm^2/C^2)
- q1 and q2 are the charges of the two point charges (in this case, q1 = 3.5 μC and q2 = -0.5 μC, where 1 μC = 1 x 10^-6 C)
- r is the distance between the point charge and the point at which the potential energy is calculated (in this case, r = d1 or d2)
Let's calculate the respective potential energies at points R and P:
PE(R) = k * q1 * q2 / r2
PE(P) = k * q1 * q2 / r1
Substituting the given values into the formulas:
PE(R) = (9 x 10^9 Nm^2/C^2) * (3.5 x 10^-6 C) * (-0.5 x 10^-6 C) / (3.5 cm)
PE(P) = (9 x 10^9 Nm^2/C^2) * (3.5 x 10^-6 C) * (-0.5 x 10^-6 C) / (8.8 cm)
Converting the distances to meters:
PE(R) = (9 x 10^9 Nm^2/C^2) * (3.5 x 10^-6 C) * (-0.5 x 10^-6 C) / (0.035 m)
PE(P) = (9 x 10^9 Nm^2/C^2) * (3.5 x 10^-6 C) * (-0.5 x 10^-6 C) / (0.088 m)
Calculating the values:
PE(R) ≈ -1.91 J
PE(P) ≈ -0.76 J
Finally, we can calculate the change in potential energy (ΔPE):
ΔPE = PE(R) - PE(P)
≈ (-1.91 J) - (-0.76 J)
≈ -1.15 J
Therefore, the change in potential energy (ΔPE) of charge q1 when it is moved from point P to point R is approximately -1.15 J.