NEB Class 11 • Physics • Electrostatics

Electric Potential, Potential Difference & Potential Energy: NEB Class 11 Physics Guide

Move from vector electric fields to scalar energy language. Distinguish V, ΔV and U; apply reference choices, point-charge superposition and conservation without losing signs.

Potential as energy per charge
Voltage, work and potential energy
Point charges, equipotentials and examples

Electric field crosses equipotentials at right angles.

Curriculum boundary

Why three similar terms are not interchangeable

The CDC secondary curriculum includes potential, potential difference, potential energy and electron volt; check the CDC Physics Grade 11 page. The definitions align with OpenStax electric potential energy and potential difference.

Review Electric Field and Work, Energy & Power first.

Three quantities

Separate source property from placed-charge energy

Quantity	Meaning	Unit
Electric potential V	U/q at a point relative to a reference	volt = J/C
Potential difference ΔV	V_final−V_initial	volt
Potential energy U	Energy of a charge configuration	joule

V belongs to the source configuration and reference choice; U=qV also depends on the placed charge. A negative q reverses the sign relation between U and V. Saying “high voltage means high energy” is incomplete without the charge amount.

Work and sign

Use conservative-force energy bookkeeping

For electrostatic forces, work depends only on endpoints. W_field=−ΔU and ΔU=qΔV. External slow movement has W_external=+ΔU when kinetic energy is unchanged.

Positive charge

A +2.0 μC charge moves from 30 V to 10 V. ΔV=−20 V and ΔU=qΔV=−40 μJ. The field does +40 μJ of work.

Negative charge

An electron moves through +100 V: ΔU=(−e)(100 V)=−100 eV=−1.602×10⁻¹⁷ J. If released from rest with only electrostatic force, kinetic energy increases by 100 eV.

The electron volt is an energy unit, not a voltage: 1 eV=1.602×10⁻¹⁹ J.

Point-source potential

Add potentials algebraically

With zero potential at infinity, a point charge gives V=kQ/r. Sign comes directly from Q. For multiple point charges, V=ΣkQᵢ/rᵢ; scalar superposition needs no component resolution.

One point charge

Q=+3.0 nC at r=0.20 m gives V≈(8.99×10⁹)(3.0×10⁻⁹)/0.20≈135 V.

Dipole midpoint

Equal +Q and −Q at equal distances give V=0 at the midpoint, but their electric fields point the same way and add. Zero potential does not imply zero field.

Energy of two charges

Two point charges have configuration energy U=kq₁q₂/r relative to infinite separation. Opposite signs give negative U, meaning external work is required to separate the bound pair slowly to infinity.

Uniform field

Relate field direction to decreasing potential

For a displacement d parallel to a uniform electric field, ΔV=−Ed. More generally ΔV=−E·d for constant E. Potential decreases in the field direction. A positive charge released from rest tends toward lower V and lower U; a negative charge tends toward higher V while its U decreases.

Parallel plates

Two plates have 600 V difference and 3.0 cm separation with an approximately uniform field. E≈|ΔV|/d=600/0.030=2.0×10⁴ V/m, the same dimensional unit as N/C.

Equipotential maps

Read contours as electric “height”

An equipotential line or surface has constant V, so moving along it gives ΔV=0 and electrostatic work zero. Electric field is perpendicular to equipotentials and points toward decreasing V. Closely spaced potential contours indicate a larger field magnitude in a comparable map.

Equipotentials do not cross when each point has one potential. A conductor in electrostatic equilibrium is an equipotential; otherwise tangential field would move free charges.

Energy conservation

Convert potential energy to kinetic energy

With only electrostatic forces, Kᵢ+Uᵢ=K_f+U_f. For a particle starting from rest, K_f=−ΔU=−qΔV when the result is positive.

Proton through 500 V

A proton accelerated through a 500 V drop gains 500 eV≈8.01×10⁻¹⁷ J. Non-relativistically, v=√(2K/m_p)≈3.10×10⁵ m/s.

Check whether the calculated kinetic energy and speed justify non-relativistic mechanics; large accelerating voltages may require a relativistic model.

Exam readiness

Common mistakes and practice tasks

Potential is scalar; electric field is vector.
Potential needs a reference choice.
ΔV is final minus initial.
Work by field is −qΔV.
Negative charge reverses U–V trend.
Zero V need not mean zero E.
Equipotentials are perpendicular to E.
Electron volt is energy, not voltage.

Find V from three point charges.
Find U of a placed positive and negative charge.
Calculate work across a potential difference.
Convert joules and eV.
Find E from parallel-plate voltage.
Interpret an equipotential map.

For online or physical NEB tuition, call 9846662070.

Frequently asked questions

Questions students ask about electric potential

What is the difference between potential and potential energy?

Potential is energy per unit charge at a point; potential energy also depends on the placed charge and is U=qV.

Why is electric potential a scalar?

It represents energy per charge, so contributions add algebraically without vector components.

Can potential be zero while field is nonzero?

Yes. At a dipole midpoint, + and − potentials cancel but field vectors add.

Which way does electric field point on a potential map?

Perpendicular to equipotentials toward decreasing potential.

Why does a negative charge move toward higher potential?

Its potential energy U=qV decreases when V increases because q is negative.

Where can I get potential tuition?

Call 9846662070 for current online or physical NEB tuition schedules and fees.

References and next steps

Sources and related study guides

Continue with the study guide and then Capacitors. Curriculum scope and sources were checked on 2 August 2026; follow current CDC, NEB and college instructions if requirements change.

Integrated transfer

Compare gravitational and electric energy landscapes

Gravitational potential near Earth can be modelled as gh per unit mass; electric potential is U/q per unit charge. Both conservative-force potentials permit endpoint energy accounting. The analogy breaks at sign: mass is positive, while electric charge can be positive or negative.

A positive charge behaves like a positive test mass in the sense that force points toward decreasing potential energy. A negative charge can move toward increasing electric potential while its potential energy decreases. State the traveller’s sign before using “uphill” or “downhill.”

Path independence

Move a +1 μC charge between points differing by −200 V. Regardless of the electrostatic path, ΔU=−200 μJ and field work +200 μJ, provided the source configuration remains fixed and non-electrostatic work is accounted separately.

Deeper connection

Recover field from changes in potential

In one dimension, E_x=−dV/dx. The minus sign says the field points toward decreasing potential. For a finite interval in a nearly uniform field, E_x≈−ΔV/Δx. In three dimensions the electric field is the negative gradient of potential, a vector built from spatial rates of change.

Potential graph

Between x=0.10 m and 0.30 m, potential falls linearly from 50 V to −10 V. E_x=−(−60 V/0.20 m)=+300 V/m. A +2 μC charge feels 0.60 mN in +x; a −2 μC charge feels the same magnitude in −x.

Potential of a continuous distribution

For distributed charge, divide it into elements dq and add dV=k dq/r. Because potential is scalar, this integral is often simpler than integrating electric-field components. Differentiate the resulting V only after symmetry and reference are clear.

Ring centre

Every element of a uniformly charged ring of total Q is distance R from its centre, so V=kQ/R there. Electric field is zero by vector symmetry, again showing that zero E and nonzero V can coexist.

Potential energy of several charges

Assemble a system one charge at a time. For point charges, U=Σ_pairskqᵢqⱼ/rᵢⱼ, counting each pair once. A common error is to double-count both i–j and j–i interactions.

Three-charge assembly

For charges q₁, q₂ and q₃, U=kq₁q₂/r₁₂+kq₁q₃/r₁₃+kq₂q₃/r₂₃. The sign of total U indicates energy relative to infinite separation, not whether every pair is attractive.

Limit checks matter: far from a compact distribution with net charge Q, leading potential approaches kQ/r. For zero net charge, leading potential falls faster and depends on the charge arrangement.

Nepal-relevant transfer: a household outlet or battery label gives potential difference, not the energy used by itself. Energy transferred depends on charge moved and circuit behaviour. Never probe mains voltage in a school experiment; use approved low-voltage sources and meters under supervision. When comparing a 1.5 V cell with a 12 V battery, state that voltage is energy per coulomb while capacity and internal resistance affect total deliverable energy and current.

Final check: change the zero-potential reference and verify that potential differences, electric fields, energy changes and work remain invariant. If a conclusion changes, an absolute V was used where only ΔV is measurable.

Use volts, joules and coulombs consistently, and report the direction of energy transfer in words.

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