Two particles with charges +8e and -8e are initially very far apart (effectively an infinite distance apart). They are then fixed at positions that are 7.07 x 10-12 m apart. What is EPEfinal - EPEinitial, which is the change in the electric potential energy?
PE₁=k•q₁•q₂/r₁
r₁=∞ =>PE₁ =0
PE₂=k•q₁•q₂/r₂
r₂= 7.07•10⁻¹² m
ΔPE= PE₂ - PE₁=PE₂=
= 9•10⁹•8e(-8e)/ 7.07•10⁻¹²=
=-9•10⁹•(8•1.6•10⁻¹⁹)² /7.07•10⁻¹²=-
=2.1•10⁻¹⁵ J
To find the change in electric potential energy (EPE), we need to calculate the final electric potential energy (EPEfinal) and the initial electric potential energy (EPEinitial) and then subtract the initial from the final.
The formula for electric potential energy is given by:
EPE = k * q1 * q2 / r
Where:
k is the electrostatic constant (k = 9 x 10^9 N m^2/C^2)
q1 and q2 are the charges of the particles (+8e and -8e)
r is the distance between the particles (7.07 x 10^-12 m)
Let's calculate EPEfinal first:
EPEfinal = k * q1 * q2 / r
EPEfinal = (9 x 10^9 N m^2/C^2) * (+8e) * (-8e) / (7.07 x 10^-12 m)
Note: Here, e is the elementary charge. We can substitute e = 1.6 x 10^-19 C.
EPEfinal = (9 x 10^9 N m^2/C^2) * (+8 * 1.6 x 10^-19 C) * (-8 * 1.6 x 10^-19 C) / (7.07 x 10^-12 m)
Now, let's calculate EPEinitial:
EPEinitial = k * q1 * q2 / r
EPEinitial = (9 x 10^9 N m^2/C^2) * (+8e) * (-8e) / (∞)
Since the particles are initially a very far distance apart, the distance between them can be considered as infinite (∞), which makes the EPEinitial equal to 0.
Therefore, EPEfinal - EPEinitial = EPEfinal - 0 = EPEfinal.
So, the change in electric potential energy is equal to the final electric potential energy, EPEfinal:
EPEfinal = (9 x 10^9 N m^2/C^2) * (+8 * 1.6 x 10^-19 C) * (-8 * 1.6 x 10^-19 C) / (7.07 x 10^-12 m)
You can now calculate the numerical value using the given values and the above equation.
To calculate the change in electric potential energy (EPE) between the initial and final states, we need to find the EPE for each state and then subtract the initial EPE from the final EPE.
The electric potential energy between two charged particles can be calculated using the formula:
EPE = k * (|q1 * q2|) / r
where k is the electrostatic constant, q1 and q2 are the charges of the particles, and r is the distance between them.
Given that the charges of the two particles are +8e and -8e, and the distance between them is 7.07 x 10^(-12) m, we can substitute these values into the formula to find the EPE for each state.
EPEinitial = k * (|+8e * -8e|) / (effectively an infinite distance)
= 0 [Since the initial distance between the particles is effectively infinite, the EPE initially is zero.]
EPEfinal = k * (|+8e * -8e|) / (7.07 x 10^(-12) m)
= k * (8e * 8e) / (7.07 x 10^(-12) m)
Now, we need to calculate the electrostatic constant k:
k = 8.99 x 10^9 N m^2 / C^2
Substituting the values:
EPEfinal = (8.99 x 10^9 N m^2 / C^2) * (8e * 8e) / (7.07 x 10^(-12) m)
After calculating EPEfinal, you can find the change in electric potential energy by subtracting EPEinitial from EPEfinal:
Change in EPE = EPEfinal - EPEinitial
Substituting the values, you can solve the equation to find the change in electric potential energy.