Two positive charges of 0.2microC and 0.01 microC are placed 10cm apart. Calculate the work done in reducing their distance to 5 cm
1.8x10*-2
The work done in reducing the distance between the charges from 10 cm to 5 cm is:
W = K * q1 * q2 * (1/r2 - 1/r1)
where:
K = Coulomb's constant = 9x10^9 N*m^2/C^2
q1 = 0.2 microC = 2x10^-7 C
q2 = 0.01 microC = 1x10^-8 C
r1 = initial distance = 10 cm = 0.1 m
r2 = final distance = 5 cm = 0.05 m
Plugging in the values, we get:
W = 9x10^9 * 2x10^-7 * 1x10^-8 * (1/0.052 - 1/0.12) = 1.8x10^-2 J
Therefore, the work done in reducing their distance to 5 cm is 1.8x10^-2 J.
To calculate the work done in reducing the distance between the two positive charges, we can use the formula for electrostatic potential energy.
The formula for the electrostatic potential energy between two point charges is given by:
U = k * (q1 * q2) / r
Where:
U is the electrostatic potential energy
k is the electrostatic constant ≈ 9 x 10^9 N·m^2/C^2
q1 and q2 are the magnitudes of the charges, in this case, 0.2 μC and 0.01 μC respectively
r is the original distance between the charges, in this case, 10 cm or 0.1 m
First, let's calculate the initial potential energy (U_initial) when the charges are 10 cm apart:
U_initial = (9 x 10^9 N·m^2/C^2) * (0.2 μC * 0.01 μC) / 0.1 m
U_initial = 9 x 10^9 * 0.002 μC^2 / 0.1 m
Now, let's calculate the final potential energy (U_final) when the charges are 5 cm apart:
U_final = (9 x 10^9 N·m^2/C^2) * (0.2 μC * 0.01 μC) / 0.05 m
U_final = 9 x 10^9 * 0.002 μC^2 / 0.05 m
The work done in reducing the distance between the charges is the difference between the initial and final potential energies:
Work done = U_initial - U_final
Substituting the values:
Work done = (9 x 10^9 * 0.002 μC^2 / 0.1 m) - (9 x 10^9 * 0.002 μC^2 / 0.05 m)
Simplifying the expression, we find the work done.