Two point charges, q1 and q2 are separated by a distance d. For convenience, we will say that q1 is at the origin (0,0) on a coordinate system, q2 is at (d,0) and a reference point p is directly above q2 at a distance h at point (d,h). q1 has value 1μ C and q2 has value 8μ C. Take d= 1.1m and h= 0.7m. Note k=9×109Nm2/C2What is the potential energy of this configuration? Give your answer in Joules, to two decimal places, but do not enter the units.
Question
Two point charges, q1 and q2 are separated by a distance d. For convenience, we will say that q1 is at the origin (0,0) on a coordinate system, q2 is at (d,0) and a reference point p is directly above q2 at a distance h at point (d,h). q1 has value 1μ C and q2 has value 8μ C. Take d= 1.1m and h= 0.7m.
Note k=9×109Nm2/C2What is the potential energy of this configuration?
Give your answer in Joules, to two decimal places, but do not enter the units.
Solution
The potential energy (U) of a system of point charges is given by the formula:
U = k * (q1*q2)/r
where:
- k is Coulomb's constant (9×10^9 Nm^2/C^2),
- q1 and q2 are the charges,
- r is the distance between the charges.
First, we calculate the potential energy between q1 and q2:
U12 = k * (q1*q2)/d U12 = 9×10^9 * (1μC * 8μC) / 1.1m U12 = 9×10^9 * (1×10^-6 C * 8×10^-6 C) / 1.1 U12 = 0.06545 J
Next, we calculate the potential energy between q1 and p. Since p is a reference point with no charge, the potential energy is 0.
Finally, we calculate the potential energy between q2 and p. Again, since p is a reference point with no charge, the potential energy is 0.
Therefore, the total potential energy of the configuration is U12, which is 0.06545 J. Rounded to two decimal places, this is 0.07 J.
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