(D) Surface charge density of the earth,$\sigma = 10^{-9} \; C\;m^{-2}$.Current over the entire globe,$I = 1800 \; A$.Radius of the earth,$r = 6.37 \t

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(D) Surface charge density of the earth,$\sigma = 10^{-9} \; C\;m^{-2}$.Current over the entire globe,$I = 1800 \; A$.Radius of the earth,$r = 6.37 \times 10^{6} \; m$.Surface area of the earth,$A = 4 \pi r^{2}$.$A = 4 \times 3.14159 \times (6.37 \times 10^{6})^{2} \approx 5.096 \times 10^{14} \; m^{2}$.Total charge on the earth's surface,$q = \sigma \times A$.$q = 10^{-9} \times 5.096 \times 10^{14} = 5.096 \times 10^{5} \; C$.Time taken to neutralize the earth's surface,$t = \frac{q}{I}$.$t = \frac{5.096 \times 10^{5}}{1800} \approx 283.11 \; s$.Using the provided options,the closest value is $282.77 \; s$.

Class 12 Physics Electric Charges and Fields Mix Examples-Electric Charges and Fields

Medium

The earth's surface has a negative surface charge density of $10^{-9} \; C\;m^{-2}$. The potential difference of $400 \; kV$ between the top of the atmosphere and the surface results (due to the low conductivity of the lower atmosphere) in a current of only $1800 \; A$ over the entire globe. If there were no mechanism of sustaining the atmospheric electric field,how much time (roughly) would be required to neutralize the earth's surface (in $; s$)? (This never happens in practice because there is a mechanism to replenish electric charges,namely the continual thunderstorms and lightning in different parts of the globe). (Radius of earth $= 6.37 \times 10^{6} \; m$.)

A
$372.94$
B
$186.34$
C
$146.37$
D
$282.77$

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Mix Examples-Electric Charges and Fields

Four charges of $1\ \mu C, 2\ \mu C, 3\ \mu C,$ and $-6\ \mu C$ are placed at the corners of a square of side $1\ m$. The square lies in the $x-y$ plane with its center at the origin.

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Find the force experienced by the semicircular rod charged with a charge $q$,placed as shown in the figure. The radius of the wire is $R$ and the line of charge with linear charge density $\lambda$ is passing through its center and is perpendicular to the plane of the wire.

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Four identical point masses,each of mass $m$ and carrying charge $+q$,are placed at the corners of a square of side $a$ on a frictionless horizontal surface. If the particles are released simultaneously,the kinetic energy of the system when they are infinitely far apart is

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Two equal negative charges are fixed at the points $(0, a)$ and $(0, -a)$ on the $y$-axis. $A$ positive charge $Q$ is released from rest at the point $(2a, 0)$ on the $x$-axis. The charge $Q$ will

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An empty thick conducting shell of inner radius $a$ and outer radius $b$ is shown in the figure. It is observed that the inner face of the shell carries a uniform charge density $-\sigma$ and the outer surface carries a uniform charge density $+\sigma$. If a point charge $q_A$ is placed at the center and another point charge $q_B$ is placed at a distance $c (> b)$ from the center of the shell,then choose the correct statement.

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Four charges of $1\ \mu C, 2\ \mu C, 3\ \mu C,$ and $-6\ \mu C$ are placed at the corners of a square of side $1\ m$. The square lies in the $x-y$ plane with its center at the origin.

Find the force experienced by the semicircular rod charged with a charge $q$,placed as shown in the figure. The radius of the wire is $R$ and the line of charge with linear charge density $\lambda$ is passing through its center and is perpendicular to the plane of the wire.

Four identical point masses,each of mass $m$ and carrying charge $+q$,are placed at the corners of a square of side $a$ on a frictionless horizontal surface. If the particles are released simultaneously,the kinetic energy of the system when they are infinitely far apart is

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