Question
Question: In the figure are shown charges \(q_{1} = 2 \times 10^{-8} C\) and \(q_{2} = -0.4 \times 10^{-8} C\)...
In the figure are shown charges q1=2×10−8C and q2=−0.4×10−8C. A charge q3=0.2×10−8C is moved along the arc of a circle from C to D. The potential energy of q3 is
a) will increase approximately by 76%
b) will decrease approximately by 76%
c) will remain same
d) will increase approximately by 12%
Solution
An object possesses electric potential energy by two elements: the charge possessed by an object itself and the relative position of an object concerning other electrically charged objects. The measurement of electric potential depends on the value of work done in transferring the object from one location to another against the electric field.
Complete step-by-step solution:
Given: q1=2×10−8C
q2=−0.4×10−8C
q3=0.2×10−8C
Initial potential energy on the q3:
Ui=r13kq3q1+r23kq3q2
Final potential energy on the q3:
Uf=r’13kq3q1+r’23kq3q2
Change in potential energy =Uf−Ui
=r13kq3q1+r23kq3q2−r’13kq3q1−r’23kq3q2
Put r13=r’13.
Therefore, change in potential energy will be:
=r23kq3q2−r’23kq3q2
Percentage of change in energy
=UiUf−Ui×100
=r13kq3q1+r23kq3q2r23kq3q2−r’23kq3q2×100
=r13q1+r23q2q2(r231−r’231)×100
r’23=0.2m, r23=1m, r13=0.8m
Put all the values in the above formula.
=0.82×10−8+1−0.4×10−8−0.4×10−8(0.21−11)×100
=2.5−0.4−0.4(5−1)×100
=2.1−1.6×100
=−76%
So, Potential energy is decreased by −76%.
Option (b) is right.
Note: When an object is pushed against the electric field, it achieves some energy, described as the electric potential energy. For a charge, the electric potential is achieved by dividing the potential energy by the amount of charge.