The magnitude of the average electric field normally present in the atmosphere just above the surface of the Earth is about $$150\,N/C,$$ directed inward towards the center of the Earth. This gives the total net surface charge carried by the Earth to be :
[Given $${\varepsilon _0} = 8.85 \times {10^{ - 12}}\,{C^2}/N - {m^2},{R_E} = 6.37 \times {10^6}m$$ ]
A.
$$ + 670\,kC$$
B.
$$ - 670\,kC$$
C.
$$ - 680\,kC$$
D.
$$ + 680\,kC$$
Answer :
$$ - 680\,kC$$
Solution :
Given,
Electric field $$E = 150\,N/C$$
Total surface charge carried by earth $$q = ?$$
According to Gauss’s law.
$$\eqalign{
& \phi = \frac{q}{{{ \in _0}}} = EA \cr
& {\text{or,}}\,\,q = { \in _0}EA = { \in _0}E\pi {r^2} = 8.85 \times {10^{ - 12}} \times 150 \times {\left( {6.37 \times {{10}^6}} \right)^2}. \cr
& \simeq 680\,KC \cr} $$
As electric field directed inward hence
$$q = - 680\,KC$$
Releted MCQ Question on Electrostatics and Magnetism >> Electric Field
Releted Question 1
A hollow metal sphere of radius $$5 cms$$ is charged such that the potential on its surface is $$10\,volts.$$ The potential at the centre of the sphere is
A.
zero
B.
$$10\,volts$$
C.
same as at a point $$5 cms$$ away from the surface
D.
same as at a point $$25 cms$$ away from the surface
Two point charges $$ + q$$ and $$ - q$$ are held fixed at $$\left( { - d,o} \right)$$ and $$\left( {d,o} \right)$$ respectively of a $$x-y$$ coordinate system. Then
A.
The electric field $$E$$ at all points on the $$x$$-axis has the same direction
B.
Electric field at all points on $$y$$-axis is along $$x$$-axis
C.
Work has to be done in bringing a test charge from $$\infty $$ to the origin
D.
The dipole moment is $$2qd$$ along the $$x$$-axis
Three positive charges of equal value $$q$$ are placed at the vertices of an equilateral triangle. The resulting lines of force should be sketched as in
A uniform electric field pointing in positive $$x$$-direction exists in a region. Let $$A$$ be the origin, $$B$$ be the point on the $$x$$-axis at $$x = + 1cm$$ and $$C$$ be the point on the $$y$$-axis at $$y = + 1cm.$$ Then the potentials at the points $$A,B$$ and $$C$$ satisfy: