Define electric potential and explain it. Write its $\mathrm{SI}$ unit and give its other units.
Define electric potential and explain it. Write its $\mathrm{SI}$ unit and give its other units.
The work required to be done against the electric field to bring a unit positive charge from infinite distance to the given point in the electric field is called the electrostatic or electric potential at that point. It is indicate by ' $\mathrm{V}$ '.
Consider a positive charge $\mathrm{Q}$ at the origin $\mathrm{O}$ and point $\mathrm{P}$ at certain distance and point $\mathrm{R}$ at infinite distance from its electric field.
Work done in brining a unit positive charge from infinity to the point $\mathrm{P}$ is the potential energy of that charge.
$\therefore$ Potential energy at $\mathrm{P}$ is $\mathrm{U}_{\mathrm{P}}$ and potential energy at point $\mathrm{R}$ is $\mathrm{U}_{\mathrm{R}}$ but $\frac{\mathrm{U}_{\mathrm{P}}-\mathrm{U}_{\mathrm{R}}}{q}$ is called electric potential difference between these points,
$\therefore \mathrm{V}_{\mathrm{P}}-\mathrm{V}_{\mathrm{R}}=\frac{\mathrm{U}_{\mathrm{P}}-\mathrm{U}_{\mathrm{R}}}{q}$
where $V_{P}$ and $V_{R}$ are potential at point $P$ and $R$.
Absolute value of electric potential has no importance only the difference in potential is important.
If we take potential to be zero at infinity then from equation $(1)$,
$\mathrm{V}_{\mathrm{P}}=\frac{\mathrm{U}_{\mathrm{P}}-\mathrm{U}_{\mathrm{R}}}{q}$
Hence, work done by an external force in bringing a unit positive charge without acceleration from infinity to a point is the electrostatic potential at that point.
Similar Questions
A cube of side $b$ has a charge $q$ at each of its vertices. Determine the potential and electric field due to this charge array at the centre of the cube.
A cube of side $b$ has a charge $q$ at each of its vertices. Determine the potential and electric field due to this charge array at the centre of the cube.
Consider an evacuated cylindrical chamber of height $h$ having rigid conducting plates at the ends and an insulating curved surface as shown in the figure. A number of spherical balls made of a light weight and soft material and coated with a conducting material are placed on the bottom plate. The balls have a radius $r \ll h$. Now a high voltage source ($HV$) is connected across the conducting plates such that the bottom plate is at $+V_0$ and the top plate at $-V_0$. Due to their conducting surface, the balls will get charged, will become equipotential with the plate and are repelled by it. The balls will eventually collide with the top plate, where the coefficient of restitution can be taken to be zero due to the soft nature of the material of the balls. The electric field in the chamber can be considered to be that of a parallel plate capacitor. Assume that there are no collisions between the balls and the interaction between them is negligible. (Ignore gravity)
(image)
($1$) Which one of the following statements is correct?
($A$) The balls will stick to the top plate and remain there
($B$) The balls will bounce back to the bottom plate carrying the same charge they went up with
($C$) The balls will bounce back to the bottom plate carrying the opposite charge they went up with
($D$) The balls will execute simple harmonic motion between the two plates
($2$) The average current in the steady state registered by the ammeter in the circuit will be
($A$) zero
($B$) proportional to the potential $V_0$
($C$) proportional to $V_0^{1 / 2}$
($D$) proportional to $V_0^2$
Give the answer quetion ($1$) and ($2$)
Consider an evacuated cylindrical chamber of height $h$ having rigid conducting plates at the ends and an insulating curved surface as shown in the figure. A number of spherical balls made of a light weight and soft material and coated with a conducting material are placed on the bottom plate. The balls have a radius $r \ll h$. Now a high voltage source ($HV$) is connected across the conducting plates such that the bottom plate is at $+V_0$ and the top plate at $-V_0$. Due to their conducting surface, the balls will get charged, will become equipotential with the plate and are repelled by it. The balls will eventually collide with the top plate, where the coefficient of restitution can be taken to be zero due to the soft nature of the material of the balls. The electric field in the chamber can be considered to be that of a parallel plate capacitor. Assume that there are no collisions between the balls and the interaction between them is negligible. (Ignore gravity)
(image)
($1$) Which one of the following statements is correct?
($A$) The balls will stick to the top plate and remain there
($B$) The balls will bounce back to the bottom plate carrying the same charge they went up with
($C$) The balls will bounce back to the bottom plate carrying the opposite charge they went up with
($D$) The balls will execute simple harmonic motion between the two plates
($2$) The average current in the steady state registered by the ammeter in the circuit will be
($A$) zero
($B$) proportional to the potential $V_0$
($C$) proportional to $V_0^{1 / 2}$
($D$) proportional to $V_0^2$
Give the answer quetion ($1$) and ($2$)
- [IIT 2016]
For given $\vec E = 2x\hat i + 3y\hat j$, find the potential at $(X, Y)$ if potential at origin is $5\, volts.$
For given $\vec E = 2x\hat i + 3y\hat j$, find the potential at $(X, Y)$ if potential at origin is $5\, volts.$
$N$ identical spherical drops charged to the same potential $V$ are combined to form a big drop. The potential of the new drop will be
$N$ identical spherical drops charged to the same potential $V$ are combined to form a big drop. The potential of the new drop will be
Six charges are placed around a regular hexagon of side length a as shown in the figure. Five of them have charge $q$, and the remaining one has charge $x$. The perpendicular from each charge to the nearest hexagon side passes through the center $O$ of the hexagon and is bisected by the side.
Which of the following statement($s$) is(are) correct in SI units?
$(A)$ When $x=q$, the magnitude of the electric field at $O$ is zero.
$(B)$ When $x=-q$, the magnitude of the electric field at $O$ is $\frac{q}{6 \pi \epsilon_0 a^2}$.
$(C)$ When $x=2 q$, the potential at $O$ is $\frac{7 q}{4 \sqrt{3} \pi \epsilon_0 a}$.
$(D)$ When $x=-3 q$, the potential at $O$ is $\frac{3 q}{4 \sqrt{3} \pi \epsilon_0 a}$.
Six charges are placed around a regular hexagon of side length a as shown in the figure. Five of them have charge $q$, and the remaining one has charge $x$. The perpendicular from each charge to the nearest hexagon side passes through the center $O$ of the hexagon and is bisected by the side.
Which of the following statement($s$) is(are) correct in SI units?
$(A)$ When $x=q$, the magnitude of the electric field at $O$ is zero.
$(B)$ When $x=-q$, the magnitude of the electric field at $O$ is $\frac{q}{6 \pi \epsilon_0 a^2}$.
$(C)$ When $x=2 q$, the potential at $O$ is $\frac{7 q}{4 \sqrt{3} \pi \epsilon_0 a}$.
$(D)$ When $x=-3 q$, the potential at $O$ is $\frac{3 q}{4 \sqrt{3} \pi \epsilon_0 a}$.
- [IIT 2022]