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

[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.

 

[TSny]

have no idea how to calculate Q.

Note that you are given the surface charge density of the sphere.

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

 

[drvrm]

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

 

[Aleksandre]

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 R_final would be radius of sphere+distance to charge?

 

[TSny]

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 R_final would be radius of sphere+distance to charge?

Yes.