Question:
Two identical charges repel each other with a force equal to $10\, mgwt$ when they are $0.6\, m$ apart in air.$( g = 10 ms^{-2} )$ The value of each charge is
Two identical charges repel each other with a force equal to $10\, mgwt$ when they are $0.6\, m$ apart in air.$( g = 10 ms^{-2} )$ The value of each charge is
Updated On: May 30, 2022
- 2 mc
- $2 \times 10^{-7}\,C$
- 2 nc
- $2 \mu C$
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The Correct Option is D
Solution and Explanation
Coulomb force is given by
$F= \frac{1}{4 \pi \varepsilon_{0}} \frac{q_{1} q_{2}}{r^{2}} $
$\therefore\left(10 \times 10^{-3}\right) \times 10= \frac{\left(9 \times 10^{9}\right) \times q^{2}}{(0.6)^{2}} $
$\left[\because q_{1}=q_{2}=q\right]$
or $q^{2} =\frac{10^{-1} \times 0.36}{9 \times 10^{9}} $
$=4 \times 10^{-12} $
$q =2 \times 10^{-6} \,C$
$=2 \,\mu \,C$
$F= \frac{1}{4 \pi \varepsilon_{0}} \frac{q_{1} q_{2}}{r^{2}} $
$\therefore\left(10 \times 10^{-3}\right) \times 10= \frac{\left(9 \times 10^{9}\right) \times q^{2}}{(0.6)^{2}} $
$\left[\because q_{1}=q_{2}=q\right]$
or $q^{2} =\frac{10^{-1} \times 0.36}{9 \times 10^{9}} $
$=4 \times 10^{-12} $
$q =2 \times 10^{-6} \,C$
$=2 \,\mu \,C$
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Concepts Used:
Electric Field
Electric Field is the electric force experienced by a unit charge.
The electric force is calculated using the coulomb's law, whose formula is:
\(F=k\dfrac{|q_{1}q_{2}|}{r^{2}}\)
While substituting q2 as 1, electric field becomes:
\(E=k\dfrac{|q_{1}|}{r^{2}}\)
SI unit of Electric Field is V/m (Volt per meter).