Show that the direction of electric field at a given is normal to the equipotential surface passing through that point.
Show that the direction of electric field at a given is normal to the equipotential surface passing through that point.
If the electric field were not normal to the equipotential surface, it would have non-zero component along the surface.
To move a unit test charge against the direction of the component of the field work would have to be done.
But this is in contradiction to the definition of an equipotential surface because the potential difference between any two points on the surface is $\Delta \mathrm{V}$ is zero so in
$\therefore$ Work $\mathrm{W}=q \Delta \mathrm{V}, \Delta \mathrm{V}=0, \therefore \mathrm{W}=0$
and work done in electric field $\overrightarrow{\mathrm{E}}$ with displacement $\vec{d} l$
$\mathrm{W}=\overrightarrow{\mathrm{E}} \cdot \overrightarrow{d l}=\mathrm{E} d l \cos \theta$ $0=\mathrm{E} d l \cos \theta$ $\therefore 0=\cos \theta \quad[\because \overrightarrow{\mathrm{E}} \neq 0, \overrightarrow{d l} \neq 0]$ $\therefore \quad \theta =\frac{\pi}{2}$
`Hence, the electric field $\overrightarrow{\mathrm{E}}$ is normal to the equipotential surface at that point.
Similar Questions
What is an equipotential surface ? Draw an equipotential surfaces for a
$(1)$ single point charge
$(2)$ charge $+ \mathrm{q}$ and $- \mathrm{q}$ at few distance (dipole)
$(3)$ two $+ \mathrm{q}$ charges at few distance
$(4)$ uniform electric field.
What is an equipotential surface ? Draw an equipotential surfaces for a
$(1)$ single point charge
$(2)$ charge $+ \mathrm{q}$ and $- \mathrm{q}$ at few distance (dipole)
$(3)$ two $+ \mathrm{q}$ charges at few distance
$(4)$ uniform electric field.
Two charges $2 \;\mu\, C$ and $-2\; \mu \,C$ are placed at points $A$ and $B\;\; 6 \;cm$ apart.
$(a)$ Identify an equipotential surface of the system.
$(b)$ What is the direction of the electric field at every point on this surface?
Two charges $2 \;\mu\, C$ and $-2\; \mu \,C$ are placed at points $A$ and $B\;\; 6 \;cm$ apart.
$(a)$ Identify an equipotential surface of the system.
$(b)$ What is the direction of the electric field at every point on this surface?
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 $x = + 1$ $cm$ and $C$ be the point on the $y$-axis at $y = + 1\,cm$. Then the potentials at the points $A$, $B$ and $C$ satisfy
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 $x = + 1$ $cm$ and $C$ be the point on the $y$-axis at $y = + 1\,cm$. Then the potentials at the points $A$, $B$ and $C$ satisfy
- [IIT 2001]
An infinite non-conducting sheet has a surface charge density $\sigma = 0.10\, \mu C/m^2$ on one side. How far apart are equipotential surfaces whose potentials differ by $50\, V$
An infinite non-conducting sheet has a surface charge density $\sigma = 0.10\, \mu C/m^2$ on one side. How far apart are equipotential surfaces whose potentials differ by $50\, V$
Three equal charges are placed at the corners of an equilateral triangle. Which of the graphs below correctly depicts the equally-spaced equipotential surfaces in the plane of the triangle? (All graphs have the same scale.)
Three equal charges are placed at the corners of an equilateral triangle. Which of the graphs below correctly depicts the equally-spaced equipotential surfaces in the plane of the triangle? (All graphs have the same scale.)