Vardaan Institute - Physics Worksheet

Topic 1: Electrostatic Potential & Potential Difference

Part I: Fill in the Blanks

The SI unit of electrostatic potential is ________.

Electrostatic potential is a ________ quantity.

The work done in bringing a unit positive charge from infinity to a point is called the electric ________ at that point.

$1 \text{ Volt} = 1 \text{ Joule} / 1$ ________.

If potential is the same everywhere, the work done in moving a charge is ________.

Part II: Multiple Choice Questions (MCQs)

Which of the following is the dimensional formula of electrostatic potential?

(a) $[ML^2T^{-2}A^{-1}]$

(b) $[ML^2T^{-3}A^{-1}]$

(d) $[ML^2T^{-3}A^{-2}]$

Work done in moving a charge of $2\text{ C}$ across a potential difference of $5\text{ V}$ is:

(a) $2.5\text{ J}$

(b) $10\text{ J}$

(d) $20\text{ J}$

A positive charge naturally moves from:

(a) Higher to lower potential

(b) Lower to higher potential

(d) In random direction

1 electron volt ($1\text{ eV}$) is equal to:

(a) $1.6 \times 10^{-19}\text{ J}$

(b) $1.6 \times 10^{19}\text{ J}$

(d) $1\text{ J}$

Part III: Match the Following

10.

Match the quantities in Column A with their appropriate unit/formula in Column B:

Column A	Column B
(P) Electrostatic Potential	(1) Coulomb
(Q) Work Done	(2) $W/q$
(R) Charge	(3) Volt
(S) Potential Difference	(4) Joules

Topic 2: Potential due to Point Charges & Systems

Part I: Fill in the Blanks

11.

The formula for potential $V$ at a distance $r$ from a point charge $q$ is ________.

12.

The electric potential on the equatorial line of an electric dipole is ________.

13.

For an electric dipole, the potential at an axial point is inversely proportional to $r^x$. The value of $x$ is ________.

14.

The constant $\frac{1}{4\pi\epsilon_0}$ has a numerical value of ________ $\text{Nm}^2/\text{C}^2$.

15.

Potential inside a hollow charged spherical conductor is ________ to the potential on its surface.

Part II: Multiple Choice Questions (MCQs)

16.

If the distance from a point charge is doubled, the potential becomes:

(a) Double

(b) Half

(d) Four times

17.

The net potential at the midpoint of two equal and opposite charges is:

(a) Maximum

(b) Zero

(d) Infinity

18.

The superposition principle states that total potential is the ________ sum of individual potentials.

(a) Vector

(b) Algebraic

(d) Logarithmic

Part III: True or False

19.

Electric potential due to a point charge varies inversely with the square of the distance. (True/False)

20.

The potential at the center of a dipole is always zero. (True/False)

Part IV: Match the Following

21.

Match the source with its correct potential formula:

Source	Formula for Potential ($V$)
(P) Point Charge	(1) $0$
(Q) Dipole (Axial)	(2) Constant (same as surface)
(R) Dipole (Equatorial)	(3) $\frac{kq}{r}$
(S) Inside Hollow Sphere	(4) $\frac{kp}{r^2}$

Topic 3: Equipotential Surfaces & E-Field Relation

Part I: Fill in the Blanks

22.

An ________ surface has the same potential at all points.

23.

Work done in moving a test charge on an equipotential surface is ________.

24.

Electric field lines are always ________ to equipotential surfaces.

25.

The mathematical relation between electric field and potential gradient is $E =$ ________.

26.

The negative sign in $E = -dV/dr$ shows that electric field points in the direction of ________ potential.

Part II: Multiple Choice Questions (MCQs)

27.

Equipotential surfaces for an isolated point charge are:

(a) Parallel planes

(b) Concentric cylinders

(d) Intersecting planes

28.

Equipotential surfaces for a uniform electric field are:

(a) Parallel planes

(b) Concentric spheres

(d) Ellipses

29.

Can two equipotential surfaces intersect?

(a) Yes

(b) No

(d) Only for negative charges

30.

If $V = 5x$ volts, the magnitude of the electric field $E$ along the x-axis is:

(a) $5\text{ V/m}$

(b) $10\text{ V/m}$

(d) Zero

Part III: True or False

31.

The surface of a charged perfect conductor is an equipotential surface. (True/False)

32.

Potential gradient is a vector quantity. (True/False)

Section D: Electrostatic Potential Energy

Part I: Fill in the Blanks

33.

The potential energy of a system of two charges is given by $U =$ ________.

34.

The SI unit of electrostatic potential energy is ________.

35.

Potential energy of a dipole in an external electric field is $U =$ ________.

36.

A dipole is in stable equilibrium when the angle between $\vec{p}$ and $\vec{E}$ is ________ degrees.

37.

Work done in rotating a dipole from $\theta_1$ to $\theta_2$ is $W =$ ________.

Part II: Multiple Choice Questions (MCQs)

38.

If two like charges are brought closer, the potential energy of the system:

(a) Increases

(b) Decreases

(d) Becomes zero

39.

If an electron and proton are brought closer, the potential energy:

(a) Increases

(b) Decreases

(d) Becomes positive

40.

The potential energy of a dipole is minimum when it is aligned:

(a) Perpendicular to E

(b) Opposite to E

(d) At $45^\circ$ to E

Part III: Match the Following

41.

Match the Dipole Alignment with its Potential Energy ($U$):

Alignment ($\theta$)	Potential Energy ($U$)
(P) $\theta = 0^\circ$ (Stable)	(1) $+pE$
(Q) $\theta = 90^\circ$	(2) $-pE$
(R) $\theta = 180^\circ$ (Unstable)	(3) $0$

Topic 4: Electrostatic Potential Energy

Part I: Fill in the Blanks

42.

Capacitance $C$ is the ratio of ________ to potential difference $V$.

43.

The SI unit of capacitance is ________.

44.

$1\mu\text{F} =$ ________ Farads.

45.

Capacitance of an isolated spherical conductor of radius $R$ is $C =$ ________.

46.

Capacitance of a parallel plate capacitor in vacuum is $C =$ ________.

47.

When a dielectric is inserted between the plates, capacitance ________.

48.

In a series combination of capacitors, ________ remains the same across each.

49.

In a parallel combination of capacitors, ________ remains the same across each.

Part II: Multiple Choice Questions (MCQs)

50.

Equivalent capacitance of $C_1$ and $C_2$ in parallel is:

(a) $C_1 + C_2$

(b) $\frac{C_1 C_2}{C_1+C_2}$

(d) $\frac{C_1+C_2}{C_1 C_2}$

51.

Equivalent capacitance of two $4\mu\text{F}$ capacitors in series is:

(a) $8\mu\text{F}$

(b) $2\mu\text{F}$

(d) $16\mu\text{F}$

52.

The energy stored in a capacitor is given by:

(a) $\frac{1}{2}CV^2$

(b) $\frac{1}{2}QV$

(d) All of these

53.

If the distance between plates of a parallel plate capacitor is halved, capacitance:

(a) Halves

(b) Doubles

(d) Remains unchanged

54.

The value of dielectric constant ($K$) for a perfect conductor is:

(a) $1$

(b) $0$

(d) $-1$

Part III: Match the Following

55.

Match the quantities with their formulas:

Quantity	Formula
(P) Energy Density ($u$)	(1) $\frac{1}{2}CV^2$
(Q) Energy Stored ($U$)	(2) $\frac{1}{2}\epsilon_0 E^2$
(R) Series Equivalent ($C_s$)	(3) $C_1 + C_2$
(S) Parallel Equivalent ($C_p$)	(4) $(\frac{1}{C_1} + \frac{1}{C_2})^{-1}$

Topic 5: Capacitance & Combinations

Part I: Fill in the Blanks

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