SATHEE: Electrostatics Question 223

Electrostatics Question 223

Question: An infinite number of charges, each of charge 1 mC, are placed on the x-axis with co-ordinates x = 1, 2, 4, 8, ….¥. If a charge of 1 C is kept at the origin, then what is the net force acting on 1 C charge [DCE 2004]

Options:

A) 9000 N

B) 12000 N

C) 24000 N

D) 36000 N

Show Answer

Answer:

Correct Answer: B

Solution:

The schematic diagram of distribution of charges on x-axis.

Total force acting on 1 C charge is given by

$F = \frac{1}{4 π ε_{0}} [\frac{1 \times 1 \times 10^{- 6}}{{(1)}^{2}} + \frac{1 \times 1 \times 10^{- 6}}{{(2)}^{2}} .$

$. + \frac{1 \times 1 \times 10^{- 6}}{{(4)}^{2}} + \frac{1 \times 1 \times 10^{- 6}}{{(8)}^{2}} + \dots . \infty]$

$= \frac{10^{- 6}}{4 π ε_{0}} (\frac{1}{1} + \frac{1}{4} + \frac{1}{16} + \frac{1}{64} + \dots \infty) = 9 \times 10^{9} \times 10^{- 6} (\frac{1}{1 - \frac{1}{4}})$

$= 9 \times 10^{9} \times 10^{- 6} \times \frac{4}{3} = 9 \times 10^{3} \times \frac{4}{3}$ = 12000 N

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Electrostatics Question 223

Question: An infinite number of charges, each of charge 1 mC, are placed on the x-axis with co-ordinates x = 1, 2, 4, 8, ….¥. If a charge of 1 C is kept at the origin, then what is the net force acting on 1 C charge [DCE 2004]

Options:

Answer:

Solution:

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