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1. Electric Charges and Fields
easy
An infinite line charge produces a field of $9 \times 10^4 \;N/C$ at a distance of $2\; cm$. Calculate the linear charge density in $\mu C / m$
A
$36$
B
$25$
C
$20$
D
$10$
Solution
Electric field produced by the infinite line charges at a distance d having linear charge density
$\lambda$ is given by the relation,
$E=\frac{\lambda}{2 \pi \varepsilon_{0} d} \Rightarrow \lambda=2 \pi \varepsilon_{0} d E$
Where, $d =2 \,cm =0.02 \,m , E =9 \times 10^{4} \,N / C$
$\varepsilon_{0}=$ Permittivity of free space and $\frac{1}{4 \pi \varepsilon_{0}}=9 \times 10^{9} Nm ^{2} C ^{-2}$
Therefore, $\lambda=\frac{0.02 \times 9 \times 10^{4}}{2 \times 9 \times 10^{9}}=10\, \mu \,C / m$
Therefore, the linear charge density is $10\; \mu \,C / m$
Standard 12
Physics
