two positive points charges of 15c and 13c are placed 12cm apart . find the work done in bringing the two charges 4cm closer.
find the Potential energy at one of the charges due to the distance and othter charge.
PE=kQ1Q2/d
What is the PE at 4 cm closer?
PE=kQ1Q2/(d-.04)
then thw work moving Q2 must be
difference in PE
W=u¹+u²
u¹=kq¹q²/d
u²=kq¹q²/d-0.5
To find the work done in bringing the two charges closer, we can use the formula:
Work = potential energy final - potential energy initial
Step 1: Calculate the initial potential energy.
The initial potential energy can be calculated using the formula:
Potential energy initial = (k * q1 * q2) / r_initial
where:
k is the electrostatic constant, approximately equal to 9 × 10^9 Nm²/C²
q1 and q2 are the charges in coulombs
r_initial is the initial distance between the charges in meters
Given:
q1 = 15 C
q2 = 13 C
r_initial = 12 cm = 0.12 m
Calculating the initial potential energy:
Potential energy initial = (9 × 10^9 Nm²/C²) * (15 C * 13 C) / 0.12 m
Step 2: Calculate the final potential energy.
The final potential energy can be calculated using the same formula as above, but with the new distance between the charges:
Potential energy final = (k * q1 * q2) / r_final
Given that the charges are brought 4 cm closer, the new distance between them is r_final = r_initial - 4 cm = 0.08 m.
Calculating the final potential energy:
Potential energy final = (9 × 10^9 Nm²/C²) * (15 C * 13 C) / 0.08 m
Step 3: Calculate the work done.
Now that we have the initial potential energy and the final potential energy, we can find the work done:
Work = Potential energy final - Potential energy initial
Substituting the calculated values:
Work = [(9 × 10^9 Nm²/C²) * (15 C * 13 C) / 0.08 m] - [(9 × 10^9 Nm²/C²) * (15 C * 13 C) / 0.12 m]
Simplifying this equation will give you the final answer, which is the work done in bringing the charges closer by 4 cm.
To find the work done in bringing the two charges closer, you need to calculate the change in potential energy. The work done is equal to the negative change in potential energy.
The formula to calculate the potential energy between two charges is given by:
U = k * (q1 * q2) / r
Where:
U = potential energy
k = Coulomb's constant (9 x 10^9 N m^2 / C^2)
q1, q2 = charges of the two points charges
r = distance between the two charges
Let's calculate the potential energy of the charges initially placed 12 cm apart:
U1 = k * (q1 * q2) / r1
= (9 x 10^9 N m^2 / C^2) * ((15 C) * (13 C)) / (0.12 m)
Next, calculate the potential energy after they are brought 4 cm closer:
U2 = k * (q1 * q2) / r2
= (9 x 10^9 N m^2 / C^2) * ((15 C) * (13 C)) / (0.08 m)
Now, calculate the change in potential energy:
ΔU = U2 - U1
Finally, the work done is equal to the negative change in potential energy:
Work = -ΔU