Two positive point charges of 12 * 10 ^-6 and 8 * 10 ^-6 respectively are placed 10 cm apart in air .the work done to bring them 4cm closer

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5.8Joule

To calculate the work done to bring the two positive point charges closer, we need to use the formula for electrostatic potential energy:

W = ΔPE

Where W is the work done, and ΔPE is the change in potential energy.

The formula for potential energy between two point charges is:

PE = k * (q1 * q2) / r

Where PE is the potential energy, k is the electrostatic constant (approximately 9 x 10^9 Nm^2/C^2), q1 and q2 are the charges of the two point charges, and r is the distance between them.

Step 1: Calculate the initial potential energy:

PE1 = k * (q1 * q2) / r1

where q1 = 12 x 10^-6 C (charge of the first point charge),
q2 = 8 x 10^-6 C (charge of the second point charge),
and r1 = 10 cm = 0.1 m (initial distance).

PE1 = (9 x 10^9 Nm^2/C^2) * (12 x 10^-6 C) * (8 x 10^-6 C) / 0.1 m

Step 2: Calculate the final potential energy:

PE2 = k * (q1 * q2) / r2

where r2 = 10 cm - 4 cm = 6 cm = 0.06 m (final distance).

PE2 = (9 x 10^9 Nm^2/C^2) * (12 x 10^-6 C) * (8 x 10^-6 C) / 0.06 m

Step 3: Calculate the change in potential energy:

ΔPE = PE2 - PE1

Step 4: Calculate the work done:

W = ΔPE

Now, let's calculate the values.

PE1 = (9 x 10^9 Nm^2/C^2) * (12 x 10^-6 C) * (8 x 10^-6 C) / 0.1 m = 8.64 J

PE2 = (9 x 10^9 Nm^2/C^2) * (12 x 10^-6 C) * (8 x 10^-6 C) / 0.06 m = 14.4 J

ΔPE = PE2 - PE1 = 14.4 J - 8.64 J = 5.76 J

Therefore, the work done to bring the two positive point charges 4 cm closer is 5.76 Joules.

To find the work done to bring the two point charges closer by 4 cm, we need to use Coulomb's Law and the concept of work.

First, let's define the variables:
q1 = 12 * 10^-6 C (charge of the first point charge)
q2 = 8 * 10^-6 C (charge of the second point charge)
r1 = 10 cm (initial distance between the charges)
r2 = r1 - 4 cm (final distance between the charges)

Coulomb's Law states that the force between two point charges is given by:

F = (k * q1 * q2) / r^2

where k is the electrostatic constant and is equal to 9 × 10^9 N m^2/C^2.

The work done to bring the charges closer is equal to the change in potential energy. The potential energy of a system of two point charges is given by:

U = (k * q1 * q2) / r

To find the work done, we need to subtract the initial potential energy (U1) from the final potential energy (U2):

Work = U1 - U2

Now, let's calculate the values step by step:

1. Calculate the initial potential energy (U1):
U1 = (k * q1 * q2) / r1

2. Calculate the final potential energy (U2):
U2 = (k * q1 * q2) / r2

3. Calculate the work done:
Work = U1 - U2

Substituting the given values into the equations:

1. U1 = (9 × 10^9 N m^2/C^2) * (12 * 10^-6 C) * (8 * 10^-6 C) / (0.1 m)

2. U2 = (9 × 10^9 N m^2/C^2) * (12 * 10^-6 C) * (8 * 10^-6 C) / (0.06 m)

3. Work = U1 - U2

After calculating the above equations, you'll find the work done to bring the charges closer by 4 cm.