# Find the amount of work to move a particle from point A to B

• Aleksandre
In summary, to calculate the work done on a point charge of q=15 nC brought from infinity to 3 cm from a charged sphere with a diameter of 15 cm and a surface charge density of 12 microC/cm2, the equation W=q(kQ/Rf) is used. The value of Rfinal should be the radius of the sphere plus the distance to the point charge. The total charge Q can be calculated by multiplying the surface charge density of the sphere by the area of the sphere.
Aleksandre

## Homework Statement

How much work should be done on a point charge of q=15 nC to bring it from infinity to a distance of 3 cm from a surface of a charged sphere? Diameter of sphere is 15 cm, its surface charge density is 12 microC/cm2

## Homework Equations

W=deltaU=q*deltaV
v=kQ/r
W=deltaU=q(kQ/Rf -kQ/Ri)

## The Attempt at a Solution

If point charge is placed in infinity then initial distance would be infinity which means kQ/Ri=0. Then we are left with equation:
W=q(kQ/Rf).
k is constant, q is known=15 nC and Rfinal=0.03 meters as given. The only uknown would be Q, e.i charged sphere. Now I have everything but have no idea how to calculate Q. Can you assist me?

Thanks.

Aleksandre said:
have no idea how to calculate Q.
Note that you are given the surface charge density of the sphere.

Your value for Rfinal is not correct. What is the physical meaning of r in V = kQ/r?

Aleksandre said:
Now I have everything but have no idea how to calculate Q. Can you assist me?

i think Q can be calculated using surface charge density ... because the total charge may be considered to be concentrated at the centre. check the theory...
only the r value has to be taken properly

Thanks for reply, so to reformulate:

Area of sphere = 4pir2 =>4*3.14*0.152
Total charge Q would equal to(?) = 0.12C/m2*Area of Sphere

Then if sphere centre can be considered as a point charge(?) the Rfinal would be radius of sphere+distance to charge?

Aleksandre said:
Thanks for reply, so to reformulate:

Area of sphere = 4pir2 =>4*3.14*0.152
Total charge Q would equal to(?) = 0.12C/m2*Area of Sphere
Yes. But note that the radius of the sphere is not 0.15 m.

Then if sphere centre can be considered as a point charge(?) the Rfinal would be radius of sphere+distance to charge?
Yes.

Aleksandre

## What is work?

Work is a measure of the amount of energy required to move an object from one location to another.

## How is work calculated?

Work is calculated by multiplying the force applied to an object by the distance it is moved in the direction of the force. The formula for work is W = F*d, where W is work, F is force, and d is distance.

## What units are used to measure work?

The standard unit of measurement for work is the joule (J). Other common units include the newton-meter (N*m) and kilocalorie (kcal).

## What factors affect the amount of work required to move an object?

The amount of work required to move an object is affected by the magnitude of the applied force, the distance the object is moved, and the angle between the force and the direction of motion.

## How is work related to energy?

Work and energy are closely related, as work is the transfer of energy from one object to another. The work done on an object is equal to the change in its energy.

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