Question 798: Electrostats & Capacitance

Question

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

Accepted Answer

To find the point where the net electric potential is zero between two charges, we use the formula for electric potential due to a point charge:
$ V = \frac{Kq}{r} $
Here, $ K $ is Coulomb's constant, $ q $ is the charge, and $ r $ is the distance from the charge.
Given:
Charge at $ A $, $ q_1 = 2 \, \mu\mathrm{C} $
Charge at $ B $, $ q_2 = -3 \, \mu\mathrm{C} $
Distance between $ A $ and $ B $, $ r_1 + r_2 = 1 \, 	ext{m} $
To locate the point where the potential is zero, let $ r_1 $ and $ r_2 $ be the distances from $ A $ and $ B $ to the point, respectively. The condition for zero potential is:
$ \frac{K(2 	imes 10^{-6})}{r_1} = \frac{K(3 	imes 10^{-6})}{r_2} $
Solving for the ratio $ \frac{r_2}{r_1} $:
$ \frac{r_2}{r_1} = \frac{3}{2} $
From the sum of the distances:
$ r_1 + r_2 = 1 $
Substitute $ r_2 = \frac{3}{2}r_1 $ into the equation:
$ r_1 + \frac{3}{2}r_1 = 1 $
$ \frac{5r_1}{2} = 1 $
$ r_1 = 0.4 \, 	ext{m} $
Hence, the distance from point $ A $ where the net potential is zero is $ 0.4 \, 	ext{m} $.

Answer

0.7 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 1 m . The distance of the point from A , where net potential is zero, is

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