Question 763: Electrostats & Capacitance

Question

Charges of $2 \mu \mathrm{C}$ and $-3 \mu \mathrm{C}$ are placed at two points A and B separated by distance of 1 m . The distance of the point from $A$ where net potential is zero is

Accepted Answer

Two charges:
$q_1 = +2\:\mu	ext{C}$ at point $A$
$q_2 = -3\:\mu	ext{C}$ at point $B$
Distance $AB = 1\:	ext{m}$
We need: Distance from $A$ where
net potential = 0
.
Step 1: Equation of potential
A point at distance $x$ from $A$ (and hence $(1-x)$ from $B$) has potential:
$ V = k\frac{q_1}{x} + k\frac{q_2}{1-x} $
We want $V=0$:
$ \frac{2}{x} + \frac{-3}{1-x} = 0 $
Step 2: Solve the equation
$ \frac{2}{x} = \frac{3}{1-x} $
Cross multiply:
$ 2(1-x) = 3x $
$ 2 - 2x = 3x $
$ 2 = 5x $
$ x = 	frac{2}{5} = 0.4 \,	ext{m} $
Step 3: Check position
$x=0.4\:	ext{m}$ is between $A$ and $B$.
Physically valid, yes.
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Answer: 0.4 m
Correct option:
C

Answer

0.667 m

Answer

0.5 m

Answer

0.4 m

Answer

0.6 m

Electrostats & Capacitance

Charges of 2 \mu \mathrm{C} and -3 \mu \mathrm{C} are placed at two points A and B separated by distance of 1 m . The distance of the point from A where net potential is zero is

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