Assume that an electric field $$\overrightarrow E = 30{x^2}\hat i$$ exists in space. Then the potential difference $${V_A} - {V_0},$$ where $${V_0}$$ is the potential at the origin and $${V_A}$$ the potential at $$x = 2\,m$$ is:
A.
$$120\,J/C$$
B.
$$-120\,J/C$$
C.
$$-80\,J/C$$
D.
$$80\,J/C$$
Answer :
$$-80\,J/C$$
Solution :
Potential difference between any two points in an electric field is given by,
$$\eqalign{
& dV = - \overrightarrow E .\overrightarrow {dx} \cr
& \int\limits_{{V_O}}^{{V_A}} {dV = - \int\limits_0^2 {30{x^2}dx} } \cr
& {V_A} - {V_O} = - \left[ {10{x^3}} \right]_0^2 = - 80J/C \cr} $$
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: