In the rectangle of the figure below, the sides have lengths 4.9 cm and 15 cm, q
ID: 1347013 • Letter: I
Question
In the rectangle of the figure below, the sides have lengths 4.9 cm and 15 cm, q1 = 5.3 C, and q2 = +2.0 C. Take V = 0 at infinity.
(a) What is the electric potential at corner A?
(b) What is the electric potential at corner B?
(c) How much work is required to move a third charge q3 = +3.0 C from B to A along a diagonal of the rectangle?
(d) Does this work increase or decrease the electric energy of the three-charge system?
increase decrease no change
e) Is more, less, or the same work required if q3 is moved along a path inside the rectangle but not on a diagonal?
(f) Is more, less, or the same work required if q3 is moved along a path outside the rectangle?
Explanation / Answer
electric potential due to a charge q at a distance of r is given by k*q/r
where k=9*10^9
part a:
at corner A, electric potential=(k*q1/0.15)+(k*q2/0.049)
=(9*10^9*(-5.3*10^(-6))/0.15)+(9*10^9*2*10^(-6)/0.049)
=49346.93 volts
part b:
at corner B, electric potential=(k*q1/0.049)+(k*q2/0.15)
=(9*10^9*(-5.3*10^(-6))/0.049)+(9*10^9*2*10^(-6)/0.15)
=-853469.38 volts
part c:
work required to move from B to A=charge *(potential at A-potential at B)
=3*10^(-6)*(49346.93-(-853469.38))=2.71 J
part d:
yes it increases the energy of the three charge system as work is added to the system for moving the charge.
e)as electric field is a conservative field, work done does not depend upon the path followed.
hence same work will be required as before.
f)as electric field is a conservative field, work done does not depend upon the path followed.
hence same work will be required as before.