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## Homework Statement

The potential caused by an array of charges in a region of space can be described by the equation V(x,y,z)=2x+xy+y

^{2}-xz

^{2}volts, where all distances are measured in metres. If a charge of 2 mC is moved from the position r

_{1}=(1,2,0)m to r

_{2}=(3,1,0), calculate the resulting change in the potential energy of the system.

Calculate the electric field associated with this potential.

Determine the force that acts on the charge when it is at position r

_{1}.

## Homework Equations

E=V/d

F=E/q

V=k*(q/r)

## The Attempt at a Solution

For the first part I did:

(delta)r=(3,1,0)-(1,2,0)=(2,-1,0)

|(delta)r)=SQRT(5)

V=(8.99*10

^{9})(2*10

^{-3}/SQRT(5))=8.04*10

^{6}J

is this correct?

Im not so confident on the above answer as the electric potential energy involves two point charges but this only includes one. Do i just square this charge to get the right answer? Also I think potential energy is U not V, any clarification on this would be great.

For the second part I did:

inputting (delta)r=(2,-1,0)m into V(x,y,z) i get:

V=2(2)+(2)(-1)+(-1)

^{2}-(2)(0)

^{2}=4-2+1=3V

Using E=V/d I get:

E=3/SQRT(5)=1.341641V/m (6dp)

Is this correct?

For the last part I did:

F=E/q=1.341641/(2*10

^{-3})=671N

Is this correct?