Two charges are located along the x-axis. One has a charge of 6.3 μC, and the second has a charge of −3.4 μC.
If the electrical potential energy associated with the pair of charges is −0.043 J,what is the distance between the charges? The value of the Coulomb constant is 8.98756 × 109 N · m2/C2 , and the acceleration due to gravity is 9.81 m/s2 .
Answer in units of m
Thank you
Each has 1/2 the total PE.
So looking at the charges...
.043/2= kQ1Q2/r solve for r.
@bobpursley is right, but don't divide potential energy by 2
Oh, I've got a shocking answer for you! But first, let's calculate it seriously. The formula for electrical potential energy is given by U = k * (q1 * q2) / r, where U is the potential energy, k is the Coulomb constant, q1 and q2 are the charges, and r is the distance between the charges.
In this case, we have U = -0.043 J, q1 = 6.3 μC, q2 = -3.4 μC, and k = 8.98756 × 10^9 N · m^2/C^2. We need to find the value of r.
Rearranging the formula, we have r = k * (q1 * q2) / U. Substituting the given values, we get r = (8.98756 × 10^9 N · m^2/C^2) * ((6.3 × 10^-6 C) * (-3.4 × 10^-6 C)) / (-0.043 J).
Calculating this expression gives us r ≈ 0.001703 m. So, the distance between the charges is approximately 0.001703 meters.
Now, let me lighten the mood a bit. If these charges were a couple, I'd say "Opposites attract!" But don't worry, they won't start a shocking relationship.
To find the distance between the charges, we can use the formula for electrical potential energy:
U = (k * |q1 * q2|) / r
where U is the electrical potential energy, k is the Coulomb constant (8.98756 × 10^9 N · m^2/C^2), q1 and q2 are the magnitudes of the charges, and r is the distance between the charges.
Given:
Charge 1 (q1) = 6.3 μC = 6.3 × 10^(-6) C
Charge 2 (q2) = -3.4 μC = -3.4 × 10^(-6) C
Potential energy (U) = -0.043 J
Let's substitute these values into the formula and solve for r:
-0.043 J = (8.98756 × 10^9 N · m^2/C^2) * |(6.3 × 10^(-6) C) * (-3.4 × 10^(-6) C)| / r
We can ignore the negative sign since distance cannot be negative.
0.043 J = (8.98756 × 10^9 N · m^2/C^2) * (6.3 × 10^(-6) C * 3.4 × 10^(-6) C) / r
Now let's simplify this expression:
0.043 J = (8.98756 × 10^9 N · m^2/C^2) * (2.142 × 10^(-11) C^2) / r
0.043 J = (1.92606 × 10^(-1) N · m^2) / r
Now let's solve for r:
r = (1.92606 × 10^(-1) N · m^2) / 0.043 J
Since 1 J = 1 N · m, we can rewrite the equation as:
r = (1.92606 × 10^(-1) N · m^2) / (0.043 N · m)
Simplifying further:
r ≈ 4.488 m
Therefore, the distance between the charges is approximately 4.488 m.