Find the work that should be done to increase the distance between two point charges with the charges of 5nC and -10nC by 5cm. The initial distance between the charges is 15cm.

To find the work done in increasing the distance between two point charges, we need to calculate the electrical potential energy before and after the change in distance. The work done is equal to the change in potential energy.

The electrical potential energy between two point charges is given by the equation:

U = k * (q1 * q2) / r

Where:
U is the electrical potential energy
k is the electrostatic constant (9 x 10^9 Nm^2/C^2)
q1 and q2 are the magnitudes of the charges
r is the distance between the charges

Given:
q1 = 5nC (5 x 10^-9 C)
q2 = -10nC (-10 x 10^-9 C)
Initial distance (r1) = 15cm (15 x 10^-2 m)
Final distance (r2) = 15cm + 5cm = 20cm (20 x 10^-2 m)

Step 1: Calculate initial potential energy (U1) using the initial distance (r1).
U1 = (k * (q1 * q2)) / r1

Step 2: Calculate final potential energy (U2) using the final distance (r2).
U2 = (k * (q1 * q2)) / r2

Step 3: Calculate the work done (W) by taking the difference between U2 and U1.
W = U2 - U1

Let's calculate the work done:
Step 1:
U1 = (9 x 10^9 Nm^2/C^2) * ((5 x 10^-9 C) * (-10 x 10^-9 C)) / (15 x 10^-2 m)

U1 = -3 x 10^-6 J

Step 2:
U2 = (9 x 10^9 Nm^2/C^2) * ((5 x 10^-9 C) * (-10 x 10^-9 C)) / (20 x 10^-2 m)

U2 = -2.25 x 10^-6 J

Step 3:
W = U2 - U1

W = (-2.25 x 10^-6 J) - (-3 x 10^-6 J)

W = 0.75 x 10^-6 J

Therefore, the work that should be done to increase the distance between the two point charges by 5cm is 0.75 x 10^-6 J.