To determine at which point along the line joining the two charges the electric potential is zero, we need to understand how electric potential due to a point charge is calculated and then apply this principle to both charges.
The electric potential,
V, at a point in space due to a point charge,
q, is given by:
V=‌where
V is the electric potential,
k is Coulomb's constant
(k=9×109Nm2∕C2),
q is the magnitude of the charge, and
r is the distance from the charge to the point at which the potential is being measured.
Given two charges,
q1=20µC=20×10−6C and
q2=−10µC=−10×10−6C, separated by
1m, to have a net electric potential of zero, the electric potentials due to each charge at a point must be equal in magnitude and opposite in sign.
Let's say the point where the potential becomes zero is at a distance
x from the
20µC charge along the line joining the charges. Consequently, this point is
1−x meters from the
−10µC charge.
Setting the absolute values of the potentials equal to each other gives us:
‌=‌Since
k and the charge magnitudes
|20×10−6| and
|−10×10−6| are constant, we can simplify this to:
‌=‌Solving for
x :
‌20(1−x)=10x‌20−20x=10x‌20=30x‌x=‌=‌Therefore,
x=0.67m.
This means that the electric potential is zero at a point
0.67m from the
20µC charge.
The correct answer is:
Option C:
0.67m from the charge
20µC.