. Two positive point charge of 12 μC and 8 μC are 10 cm apart. The work done in bringing them 4 cm closer is,
To calculate the work done in bringing the two point charges closer, we need to use the formula for electric potential energy:
Work = ΔPE = PE_initial - PE_final
The electric potential energy (PE) of a pair of point charges is given by:
PE = (k * q1 * q2) / r
Where k is the electrostatic constant (9 x 10^9 N m^2/C^2), q1 and q2 are the magnitudes of the charges, and r is the distance between the charges.
Initially, the charges are 10 cm apart, so we can calculate the initial potential energy (PE_initial) using the given charges (12 μC and 8 μC) and distance (10 cm).
PE_initial = (9 x 10^9 N m^2/C^2) * (12 x 10^-6 C) * (8 x 10^-6 C) / (10 x 10^-2 m)
Now, we bring the charges 4 cm closer, resulting in a new distance of 6 cm. Using this new distance (6 cm), we can calculate the final potential energy (PE_final).
PE_final = (9 x 10^9 N m^2/C^2) * (12 x 10^-6 C) * (8 x 10^-6 C) / (6 x 10^-2 m)
Finally, we can substitute the values into the formula for work to find the work done in bringing the charges closer:
Work = ΔPE = PE_initial - PE_final
Calculate the values for PE_initial and PE_final using the given formula, and then subtract PE_final from PE_initial to find the answer.