Question

A charge of `-5 C` is at the origin. How much energy would be applied to or released from a `4 C` charge if it is moved from `(-5, 3 )` to `(2 ,-7 )`?

Answer 1

`W=6.12*10^9" Joules"`
`"since The Potential of the point B is greater than the potential"`
`"of the point of A, work is done by an external electrical force. "`

Explanation:

`"Since The electrical force is conservative,it is not important"`
`"that the charge have gone from A to B by which path.(f or c)."` `"Work doing both situation is the same."`

`"Since a charge of 4C moves in the electric field of the charge -5C,"`
`"we should find the potentials of the points A and B."`

`V_a=-k*5/(r_a)" , "V_b=-k5/(r_b)`

`r_a=sqrt((-5)^2+3^2)=sqrt(25+9)=sqrt(34)=5.83`

`r_b=sqrt(2^2+(-7)^2)=sqrt(4+49)=sqrt(53)=7.28`

`W=Q(V_b-V_a)`

`W=4(-k*5/r_b+k*5/r_a)`

`W=4*5k(1/r_a-1/r_b)`

`W=20k((r_b-r_a)/(r_a*r_b))`

`W=20k((7.28-5.83)/(7.28*5.83))`

`k=9*10^9`

`W=20k(0.034)`

`W=0.68*9*10^9`

`W=6.12*10^9" Joules"`