Four identical charges (+4.0 uC each) are brought from infinity and fixed to a straight line. The charges are located 0.33m apart. Determine the electric potential energy of this group.
PE=(13/3)k(Q^2)/a
Add up the work required to bring the charges into their places, one at a time.
Let the charge separation for adjacent charges be a = 0.33 m
The Coulomb constant is k, and each charge is Q = 4*10^-6 C
First charge: work = 0
Second charge: work = kQ/a
Third charge: work = kQ/a + kQ/(2a)
Fourth charge: work = kQ/a + kQ/(2a) + kQ/(3a)
Add them for the total potential energy
PE = (13/3) kQ/a
To determine the electric potential energy of the group of charges, we can use the formula for the electric potential energy of a system of charges:
Potential Energy = k * q1 * q2 / r
Where:
- k is the electrostatic constant, approximately equal to 8.99 × 10^9 N.m^2/C^2
- q1 and q2 are the charges
- r is the distance between the charges
First, let's calculate the total electric potential energy of the group. The charges are identical and symmetrical, so we need to consider the potential energy between each pair of adjacent charges and sum them up.
Potential Energy = 2 * (k * q^2 / r)
Since we have four identical charges, we need to multiply by 4 to calculate the total potential energy.
Potential Energy = 4 * (k * q^2 / r)
Now we can substitute the given values:
k = 8.99 × 10^9 N.m^2/C^2
q = 4.0 × 10^-6 C
r = 0.33 m
Potential Energy = 4 * (8.99 × 10^9 N.m^2/C^2) * (4.0 × 10^-6 C)^2 / 0.33 m
Calculating this expression will give us the electric potential energy of the group of charges.