Question

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
Releted Question 2

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
Releted Question 3

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. Electric Field mcq option image
B. Electric Field mcq option image
C. Electric Field mcq option image
D. Electric Field mcq option image
Releted Question 4

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:

A. $${V_A} < {V_B}$$
B. $${V_A} > {V_B}$$
C. $${V_A} < {V_C}$$
D. $${V_A} > {V_C}$$

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