Four 50-\mu {\rm{C}} charges are brought from far apart onto a line where they're spaced at 2.0-{\rm cm} intervals. How much work does it take to assemble this charge distribution?

I answered a very similar question earlier today... only the separation distance was different. Use the same method, and the formula derived there:

http://www.jiskha.com/display.cgi?id=1265240265

Well, assembling charges is no easy task! It's like putting together a puzzle, but instead of the pieces fitting nicely, they repel each other like high school classmates at a social gathering. So, let's calculate the work required using a little clown humor.

First, let's convert the distance between charges into meters. 2.0 cm is the same as 0.02 m. (I know, I know, it's a regular party trick.)

Now, the work done to assemble this charge distribution can be calculated using the formula: W = ∑(k * q1 * q2) / r, where W is the work done, k is the electrostatic constant (around 8.99 x 10^9 Nm²/C²), q1 and q2 are the charges, and r is the distance between them.

Since all the charges are the same (+50 μC or 50 * 10^(-6)) and they are all at the same distance (0.02 m), we can simplify the formula to:

W = (k * q^2) / r

Plugging in the values, we get:

W = (8.99 x 10^9 Nm²/C²) * (50 * 10^(-6) C)^2 / 0.02 m

Calculating all of that, we find the work required to assemble this charge distribution to be a whopping value. But hey, let's add a little clown twist to it:

Drumroll, please...

The work required to assemble this charge distribution is approximately [insert drumroll sounds] a mind-boggling number of joules! It's like trying to bring together a group of clowns in a tiny car – it takes a lot of effort and a touch of clown magic!

Remember, this is just a humorous way to explain the concept. The actual value of the work can be calculated using the given formula.

To calculate the work required to assemble this charge distribution, we need to consider the electrostatic potential energy.

The electrostatic potential energy between two point charges is given by the formula:

U = k * (q1 * q2) / r

where U is the potential energy, k is the electrostatic constant (8.99 * 10^9 Nm^2/C^2), q1 and q2 are the charges involved, and r is the distance between them.

In this case, we have four charges of 50 µC each. The distance between each pair of charges is 2.0 cm, or 0.02 m.

First, let's calculate the potential energy between each pair of charges:

U1 = k * (q1 * q2) / r1

U2 = k * (q2 * q3) / r2

U3 = k * (q3 * q4) / r3

Now, let's calculate the total potential energy by summing up the individual potential energies:

U_total = U1 + U2 + U3

U_total = k * (q1 * q2) / r1 + k * (q2 * q3) / r2 + k * (q3 * q4) / r3

Finally, we can substitute the given values and calculate the work required:

U_total = (8.99 * 10^9 Nm^2/C^2) * (50 * 10^(-6) C)^2 / (0.02 m) + (8.99 * 10^9 Nm^2/C^2) * (50 * 10^(-6) C)^2 / (0.02 m) + (8.99 * 10^9 Nm^2/C^2) * (50 * 10^(-6) C)^2 / (0.02 m)

U_total ≈ 4.47 J

Therefore, it would take approximately 4.47 Joules of work to assemble this charge distribution.

To calculate the work required to assemble this charge distribution, we need to consider the electric potential energy of each charge and the work done to bring each charge to its position.

The electric potential energy between two charges q1 and q2, separated by a distance r, is calculated using the formula:

U = k * (q1 * q2) / r

Where:
- U is the electric potential energy
- k is Coulomb's constant (9 x 10^9 Nm^2/C^2)
- q1 and q2 are the charges
- r is the distance between the charges

In this case, we have four charges with a spacing of 2.0 cm intervals. Let's number them as q1, q2, q3, and q4.

The work required to assemble the charge distribution is equal to the sum of the electric potential energy of each pair of charges.

Work = U12 + U23 + U34

U12 = k * (q1 * q2) / r12
U23 = k * (q2 * q3) / r23
U34 = k * (q3 * q4) / r34

where r12 = r23 = r34 = 2.0 cm = 0.02 m

Now, let's substitute the given values into the equation:

Work = (k * (q1 * q2) / r12) + (k * (q2 * q3) / r23) + (k * (q3 * q4) / r34)

Work = (9 x 10^9 Nm^2/C^2) * [(q1 * q2) / (0.02 m)] + [(q2 * q3) / (0.02 m)] + [(q3 * q4) / (0.02 m)]

As we don't have the specific values for q1, q2, q3, and q4, we cannot calculate the exact value of the work required to assemble this charge distribution. However, you can substitute the values of the charges and distance between them into the equation to calculate the work.