The potential energy of the interaction between two charges when the distance changes from 10 cm to 20 cm is halved. The exact change in potential energy requires calculating the initial potential energy with the given charges and then dividing by 2.
The question involves understanding how the potential energy of the interaction between two point charges changes when the distance between them is altered. According to Coulomb's Law, the potential energy (U) between two point charges is given by:
U = k * q1 * q2 / r
Where:
k is Coulomb's constant (8.99 x 109 N m2/C2),
q1 and q2 are the magnitudes of the two charges,
r is the distance between the charges.
Given that the only variable changing is the distance (r), which is increasing from 10 cm to 20 cm, we can compare the initial and final potential energies to find the change in potential energy. If we let U1 be the initial potential energy and U2 the final potential energy, then:
U1 = k * q1 * q2 / r1
U2 = k * q1 * q2 / r2
Since r1 is 10 cm and r2 is 20 cm, r2 is twice r1, so:
U2 = k * q1 * q2 / (2 * r1)
U2 = U1 / 2
Thus, the potential energy of the interaction between the charges when the distance is 20 cm is half of what it was at 10 cm. To find the exact change in potential energy, you would calculate U1 with the given charge values and then divide by 2 for U2.