Two positive charges of 12 µC and 8 µC respectively are 10 cm apart. Find the work done in bringing them 4 cm closer, so that, they are 6 cm apart..
find the difference in PE in the two locations.
Hold one charge stationary.
PEtotal= kQQ/.1
PE(new total)=KQQ/.06
subtract the first from the second, that must equal the work done.
There are more difficult ways to work this, involving finding work in an integral calculus equation (work= INT force*dr)
5.8 j
4.8J
To find the work done in bringing the charges closer, we need to calculate the electric potential energy before and after the movement.
The formula for electric potential energy is given by:
PE = k * (Q1 * Q2) / r,
where PE is the electric potential energy, k is the Coulomb's constant (k ≈ 8.99 × 10^9 N m^2/C^2), Q1 and Q2 are the charges, and r is the distance between the charges.
Let's calculate the initial electric potential energy when the charges are 10 cm apart.
PE_initial = k * (Q1 * Q2) / r_initial,
where r_initial = 10 cm = 0.1 m.
Substituting the values, we have:
PE_initial = (8.99 × 10^9 N m^2/C^2) * (12 × 10^(-6) C) * (8 × 10^(-6) C) / 0.1 m.
Next, we need to calculate the final electric potential energy when the charges are 6 cm apart.
PE_final = k * (Q1 * Q2) / r_final,
where r_final = 6 cm = 0.06 m.
Substituting the values, we have:
PE_final = (8.99 × 10^9 N m^2/C^2) * (12 × 10^(-6) C) * (8 × 10^(-6) C) / 0.06 m.
Finally, we can calculate the work done in bringing the charges closer:
Work done = PE_initial - PE_final.
Let's calculate it step by step:
PE_initial = (8.99 × 10^9 N m^2/C^2) * (12 × 10^(-6) C) * (8 × 10^(-6) C) / 0.1 m.
PE_final = (8.99 × 10^9 N m^2/C^2) * (12 × 10^(-6) C) * (8 × 10^(-6) C) / 0.06 m.
Work done = PE_initial - PE_final.
Calculating the values, we can find the work done in bringing the charges closer.