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Physics Question on Electric Field

An infinitely long thin straight wire has uniform charge density of 14×10−2cm−1.\frac {1}{4} \times 10^{-2} cm^{-1}. What is the magnitude of electric field at a distance 20 cm20\, cm from the axis of the wire ?

A

1.12×108 NC−11.12 \times 10^8 \,NC^{-1}

B

4.5×108 NC−14.5 \times 10^8 \,NC^{-1}

C

2.25×108 NC−12.25 \times 10^8 \,NC^{-1}

D

9×108 NC−19 \times 10^8 \,NC^{-1}

Answer

2.25×108 NC−12.25 \times 10^8 \,NC^{-1}

Explanation

Solution

We know that
E=λ2πε0rE=\frac{\lambda}{2 \pi \varepsilon_{0} r}
=14×10−210−2×18×109×5=\frac{1}{4} \times \frac{10^{-2}}{10^{-2}} \times 18 \times 10^{9} \times 5
=2.25×108N/C=2.25 \times 10^{8} N / C