Two positive point charge of 12 ?C and 8 ?C are 10 cm apart. The work done in bringing them 4 cm closer is...
So move either charge 4 cm.
I assume you have calculus
work=INT force*dx from .1 to .06 m
work= int kq1q2dx/x^2 over limits
= kq1q2/x over limits
= kqq(1/.04 - 1/.1)
= kqq(.1-.04)/.004
= kqq(.06/.004)
5.8 j
To find the work done in bringing the charges 4 cm closer, we need to calculate the change in potential energy.
The potential energy (U) between two point charges can be calculated using the formula:
U = k * (q1 * q2) / r
where:
U is the potential energy between the charges,
k is the electrostatic constant (9 x 10^9 Nm^2/C^2),
q1 and q2 are the magnitudes of the charges, and
r is the distance between the charges.
Given:
q1 = 12 μC (12 x 10^-6 C),
q2 = 8 μC (8 x 10^-6 C),
r1 = 10 cm (10 x 10^-2 m), and
r2 = 6 cm (6 x 10^-2 m).
To find the initial potential energy (U1) of the charges, substitute the given values into the formula:
U1 = k * (q1 * q2) / r1
U1 = (9 x 10^9 Nm^2/C^2) * (12 x 10^-6 C) * (8 x 10^-6 C) / (10 x 10^-2 m)
Now, calculate U1.
U1 = 9 x 12 x 8 / 10
Next, calculate the final potential energy (U2) when the charges are brought 4 cm closer:
U2 = k * (q1 * q2) / r2
U2 = (9 x 10^9 Nm^2/C^2) * (12 x 10^-6 C) * (8 x 10^-6 C) / (6 x 10^-2 m)
Now, calculate U2.
U2 = 9* 12* 8 / 6
The work done (W) in bringing the charges 4 cm closer is given by the change in potential energy:
W = U1 - U2
Calculate W.
W = U1 - U2
Finally, calculate the work done.