Practicing Success

Target Exam

CUET

Subject

Physics

Chapter

Electric Charges and Fields

Question:

Supposing that the earth has a surface charge density of 1 electron/m2; calculate electric field just outside earth's surface.

The electronic charge is $-1.6 \times 10^{-19} C$ and earth's radius is $6.4 \times 10^6 m$.  $\left(\varepsilon_0=8.9 \times 10^{-12} C^2 / N-m^2\right)$

Options:

$-1.8 \times 10^{-8}$ N/C

$+1.8 \times 10^{-8}$ N/C

$-1.8 \times 10^{-9}$ N/C

$+1.8 \times 10^{-9}$ N/C

Correct Answer:

$-1.8 \times 10^{-8}$ N/C

Explanation:

Again, the electric field E just outside the earth's surface is same is if the entire charge q were concentrated at this centre. Thus

$E=\frac{1}{4 \pi \varepsilon_0} \frac{q}{R^2}=\frac{1}{4 \pi \varepsilon_0} \frac{4 \pi R^2 \sigma}{R^2}=\frac{\sigma}{\varepsilon_0}$

Substituting the given value:

$E =\frac{\left(-1.6 \times 10^{-19}\right) C / m^2}{8.9 \times 10^{-12} C^2 / N-m^2}$

$= -1.8 \times 10^{-8}$ N/C

The minus sign indicates that E is radially inward.