Define potential energy of a point charge in a uniform electric field E → . Obtain the expression U = - P → · E → for the potential energy of a dipole of moment P → in a uniform electric field E → .

The electric potential energy of any given charge or system of changes is termed as the total work done by an external agent in bringing the charge or the system of charges from infinity to the present configuration without undergoing any acceleration. In case of electric dipole amount of work done for small angular displacement dθ , d W = τ d θ And the total work done for rotaion of dipole in uniform electric field W = ∫ θ 1 θ 2 𝜏 dθ = ∫ θ 1 θ 2 pE sin θ dθ = pE ∫ θ 1 θ 2 sin θ dθ = PE - cos θ θ 1 θ 2 = - PE cosθ 2 - cosθ 1 This amount of work done represents the potential energy stored in electric dipole i . e . U = PE cos θ 1 - cos θ 2 if θ 1 = 90 ° , θ 2 = θ , then U = PE cos 90 ° - cosθ ⇒ U = - PEcosθ ⇒ U = - P → . E →

E M B I B E

NOOTAN ISC PHYSICS Class 12 Part-1>Chapter 3 - Electric Potential>QUESTIONS>Q 1

HARD

12th ICSE

IMPORTANT

Earn 100

Show that electric potential at a point $P$ , at a distance $r$ from a fixed point charge $Q$ is given by $V = \frac{1}{4 {πε}_{0}} \frac{Q}{r}$

Important Questions on Electric Potential

HARD

12th ICSE

IMPORTANT

NOOTAN ISC PHYSICS Class 12 Part-1>Chapter 3 - Electric Potential>QUESTIONS>Q 2

Define potential difference between two points in an electric field. Derive the relation between electric field and potential difference.

MEDIUM

12th ICSE

IMPORTANT

NOOTAN ISC PHYSICS Class 12 Part-1>Chapter 3 - Electric Potential>QUESTIONS>Q 3

What is an equipotential surface? Draw the same for a point charge. Show that electric field is always directed perpendicular to an equipotential surface.

HARD

12th ICSE

IMPORTANT

NOOTAN ISC PHYSICS Class 12 Part-1>Chapter 3 - Electric Potential>QUESTIONS>Q 4

What do you mean by the potential energy of a system of charges? Derive energy expression for two point charges separated by a distance. Generalise the result for a system of

n

point charges.

HARD

12th ICSE

IMPORTANT

NOOTAN ISC PHYSICS Class 12 Part-1>Chapter 3 - Electric Potential>QUESTIONS>Q 5

Derive an expression for the total work done in rotating an electric dipole through an angle

θ

in a uniform electric field.

HARD

12th ICSE

IMPORTANT

NOOTAN ISC PHYSICS Class 12 Part-1>Chapter 3 - Electric Potential>QUESTIONS>Q 6

Define potential energy of a point charge in a uniform electric field

\vec{E}

. Obtain the expression

U = - \vec{P} \cdot \vec{E}

for the potential energy of a dipole of
moment

\vec{P}

in a uniform electric field

∴ [V = \frac{1}{4 {πε}_{0}} \cdot \frac{Q}{r}] v

.

HARD

12th ICSE

IMPORTANT

NOOTAN ISC PHYSICS Class 12 Part-1>Chapter 3 - Electric Potential>QUESTIONS>Q 7

Obtain an expression for electric potential

' V'

at a point in an end-on position

i . e

, axial position of an electric dipole.

HARD

12th ICSE

IMPORTANT

NOOTAN ISC PHYSICS Class 12 Part-1>Chapter 3 - Electric Potential>QUESTIONS>Q 8

Define electric potential. Prove that at a point in the broad-side-on position of an electric dipole the electric potential is zero.

HARD

12th ICSE

IMPORTANT

NOOTAN ISC PHYSICS Class 12 Part-1>Chapter 3 - Electric Potential>QUESTIONS>Q 1

Define electric potential. Write its SI unit and give an example in which electric potential is zero, but electric field is not zero and also give an example in which electric potential is non-zero or uniform, but electric field is zero.