Question
Write a note on equipotential surface.
✓
Answer
"An imaginery surface, any surface that have same electric potential at every point on it is called equipotential surface."
$\rightarrow $ Electric potential at distance $r$ from a point charge $q$,
$V =\frac{1}{4 \pi \varepsilon_0} \cdot \frac{q}{r} \text { If } r \text { is constant then }$
$V =\text { const. also }$
$\rightarrow $ Hence, equipotential surface for a point charge $q$ are different spheres having charge $q$ at centre, and having different radii. $($Fig. a$)$
$\rightarrow $ For such two different equipotential surfaces, potential will be different but potential for all points on any one equipotential surface will be same.
$\rightarrow $ Electric field lines for a point charge are radial lines starting $($originating$)$ from the charge and ending at infinity. $($or in negative charge.$)$
So we can say that electric field lines are perpendicular to equipotential surface.
$\rightarrow $ If the electric field is not perpendicular to the equipotential surface then there will be a component of $\overrightarrow{ E } ($electric field$)$ parallel to the surface. Which shows work needs to be done in moving the unit test charge against this component of electric field, which is against the definition of equipotential surface.
$\rightarrow $ Electric potential difference between any two points on the equipotential surface is zero. $( V = 0 )$
so, no work is required to be done in moving test charge on the surface.
$\rightarrow $ Hence electric field at each point on the equipotential surface must be perpendicular to the surface.
$\rightarrow $ Equipotential surfaces for uniform electric field are shown in fig. $C .$
$\rightarrow $ If the field is along $X-$direction, equipotential surface must be parallel to $YZ -$ plane.
$\rightarrow $ Electric potential at distance $r$ from a point charge $q$,
$V =\frac{1}{4 \pi \varepsilon_0} \cdot \frac{q}{r} \text { If } r \text { is constant then }$
$V =\text { const. also }$
$\rightarrow $ Hence, equipotential surface for a point charge $q$ are different spheres having charge $q$ at centre, and having different radii. $($Fig. a$)$
$\rightarrow $ For such two different equipotential surfaces, potential will be different but potential for all points on any one equipotential surface will be same.
$\rightarrow $ Electric field lines for a point charge are radial lines starting $($originating$)$ from the charge and ending at infinity. $($or in negative charge.$)$
So we can say that electric field lines are perpendicular to equipotential surface.
$\rightarrow $ If the electric field is not perpendicular to the equipotential surface then there will be a component of $\overrightarrow{ E } ($electric field$)$ parallel to the surface. Which shows work needs to be done in moving the unit test charge against this component of electric field, which is against the definition of equipotential surface.
$\rightarrow $ Electric potential difference between any two points on the equipotential surface is zero. $( V = 0 )$
so, no work is required to be done in moving test charge on the surface.
$\rightarrow $ Hence electric field at each point on the equipotential surface must be perpendicular to the surface.
$\rightarrow $ Equipotential surfaces for uniform electric field are shown in fig. $C .$
$\rightarrow $ If the field is along $X-$direction, equipotential surface must be parallel to $YZ -$ plane.
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
A spectroscopic instrument can resolve two nearby wavelengths $\lambda$ and $\lambda+\Delta\lambda$ if $\frac{\lambda}{\Delta\lambda}$ is smaller than 8000. This is used to study the spectral lines of the Balmer series of hydrogen. Approximately how many lines will be resolved by the instrument?
→How much positive and negative charge is there in a cup of water?
Each of the resistances shown in figure. has a value of $20\Omega.$ Find the equivalent resistance between A and B. Does it depend on whether the point A or B is at higher potential?
→Why is the de Broglie wavelength associated with macroscopic objects (cricket ball, car, etc.) not observed in daily life?
Write statement of Lenz's law of electromagnetism. A 2 m long straight vertical wire is falling perpendicularly to horizontal component at speed of 5 $m / s$ in the magnetic field of earth of $0.3 \times 10^{-4} T$. Calculate the magnitude of instantaneous value of induced emf across the ends of the wire.
→Provide the classification of solids on the basis of the relative values of electrical conductivity $(\sigma)$ or resistivity $(\rho).$
→State the underlying principle of a cyclotron. Write briefly how this machine is used to accelerate charged particles to high energies.
Answer the following questions: The angle subtended at the eye by an object is equal to the angle subtended at the eye by the virtual imae produced by a magnifying glass. In what sense then does a magnifying glass provide angular magnification?
A nucleus with mass number A=240 and BE/A = 7.6 MeV breaks into two fragments each of A = 120 with BE/A = 8.5 MeV. Calculate the released energy.
A photographic film is coated with a silver bromide layer. When light fells on this film, silver bromide molecules dissociate end the film records the light there. A minimum of $0.6eV$ is needed to dissociate a silver bromide molecule. Find the maximum wavelength of light that can be recorded by the film.
→