A 1.0 × 10−6 C test charge is 40.0cm from a 3.2 × 10−3 C charged sphere. How much work was
required to move it there from a point 1.0 × 102 cm away from the sphere?
what formula(s) should be used to calculate work...?
To calculate the work required to move the test charge from one point to another, you can use the formula for electrical potential energy, which is given by:
ΔPE = q * ΔV
where ΔPE is the change in electrical potential energy, q is the charge, and ΔV is the change in voltage.
The change in electrical potential energy can also be expressed as the negative of the work done, so we have:
Work = -ΔPE
In this case, since the test charge is moving from a point 1.0 × 10^2 cm away to a point 40.0 cm away from the charged sphere, we need to calculate the change in electrical potential energy.
The formula for electrical potential energy due to a point charge is given by:
PE = k * (q1 * q2) / r
where PE is the electrical potential energy, k is Coulomb's constant (9.0 × 10^9 Nm^2/C^2), q1 and q2 are the charges, and r is the distance between the charges.
In this scenario, q1 represents the charged sphere (3.2 × 10^-3 C) and q2 represents the test charge (1.0 × 10^-6 C), and r1 and r2 are the distances from the sphere.
Therefore, to calculate the work required to move the test charge from one point to another, we can use the following steps:
1. Calculate the electrical potential energy at the initial point (1.0 × 10^2 cm away) using the formula PE = k * (q1 * q2) / r.
2. Calculate the electrical potential energy at the final point (40.0 cm away) using the same formula.
3. Find the change in electrical potential energy by subtracting the initial potential energy from the final potential energy.
4. Take the negative of the change in electrical potential energy to find the work required to move the test charge.
These calculations will give you the answer to the question.