Question

What is the flux through a cube of side $$a$$ if a point charge of $$q$$ is at one of its corner?

A. $$\frac{{2q}}{{{\varepsilon _0}}}$$
B. $$\frac{q}{{8{\varepsilon _0}}}$$  
C. $$\frac{q}{{{\varepsilon _0}}}$$
D. $$\frac{q}{{2{\varepsilon _0}}}6{a^2}$$
Answer :   $$\frac{q}{{8{\varepsilon _0}}}$$
Solution :
According to Gauss's law, the electric flux through a closed surface is equal to $$\frac{1}{{{\varepsilon _0}}}$$  times the net charge enclosed by the surface.
As the charge enclosed $$ = \frac{q}{8}$$
So, electric flux $$ = \frac{{{q_{{\text{enclosed}}}}}}{{{\varepsilon _0}}} \Rightarrow \phi = \frac{q}{{8{\varepsilon _0}}}$$

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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Electric Field


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