CUET 2026 Most Important Physics Formulas: Complete Sheet

Physics in CUET UG 2026 emphasises quick application over theory, where the right formula at the right moment matters. You struggle not because you lack conceptual clarity, but because recalling formulas under pressure becomes difficult. A well-revised formula sheet saves time, boosts accuracy, and significantly improves overall exam final performance.

Read on to get the complete formula sheet covering the formulas of concepts from electricity to modern physics.

Electric Charges and Fields

Electricity begins with understanding how charges behave and interact in space. Concepts like Coulomb’s law, electric field, and Gauss’s law help explain forces between charges and field distributions. These ideas form the backbone for solving numerical problems and building clarity for advanced electrical topics.

• Quantization of Charge: Total charge q on a body is an integral multiple of the electronic charge e.

• q = ne

• Coulomb's Law: Describes the force between two point charges.

• In vacuum: F = 1 / 4πϵ₀ q₁q₂ / r²

• In a medium: F = 1 / 4πϵ₀k q₁q₂ / r²

• Electric Field (E): Force per unit charge.

• Definition: E = F / q

• Due to a point charge: E = 1 / 4πϵ₀ q / r²

• Force on a charge q₀ in an electric field: F = q₀E

• Electric Dipole: Two equal and opposite charges separated by a small distance.

• Dipole Moment (p): Charge × 2l. Direction is from negative to positive charge.

• Electric Field due to a Dipole:

• Axial Position: E = 1 / 4πϵ₀ (2p / r³)

• Equatorial Position: E = 1 / 4πϵ₀ (p / r³)

• Torque on a Dipole in Electric Field:

• τ = pE sinθ (Vector product of dipole moment and electric field).

• Electric Flux (Φ): Scalar product of electric field and area vector.

• Φ = E ⋅ A = EA cosθ (A scalar quantity).

• Gauss's Law: Relates electric flux to the charge enclosed.

• Φ = Q_enclosed / ϵ₀

• Electric Field due to Charge Distributions:

• Infinite Line Charge: E = λ / 2πϵ₀r (Inversely proportional to distance).

• Infinite Plane Sheet: E = σ / 2ϵ₀ (Does not depend on distance).

• Electric Field due to Spheres:

• Thin Spherical Shell: Inside E = 0; Outside E ∝ 1/R²; Surface field is constant.

• Solid Sphere: Inside E ∝ R; Outside E ∝ 1/R².

Electric Potential and Capacitance

Understanding how electrical energy is stored and transferred is essential for mastering electrostatics. Electric potential, potential difference, and capacitance explain how work is done in moving charges and how energy is stored in devices like capacitors, making this area highly relevant for application-based questions.

• Electric Potential (V): Work done in bringing a unit positive charge from infinity to a point.

• V = W / q = 1 / 4πϵ₀ q / r (A scalar quantity).

• Potential Difference (ΔV): Work done per unit charge.

• ΔV = W_AB / q₀

• Work Done: W = q × ΔV

• Potential Gradient: E = -dV/dr

• Potential Energy (U):

• U = 1 / 4πϵ₀ q₁q₂ / r (For a system of charges).

• Potential Energy of a Dipole: U = -pE cosθ

• Work Done in Rotating a Dipole: W = pE (cosθ₁ - cosθ₂)

• Capacitance (C): Ability to store electric charge.

• q = CV

• Capacitance of Conductors:

• Parallel Plate Capacitor: C = ϵ₀A / d

• Spherical Capacitor: C = 4πϵ₀ ab / (b - a) (b = outer radius, a = inner radius).

• Cylindrical Capacitor: C = 2πϵ₀l / ln(b/a)

• Combinations of Capacitors:

• Series and Parallel formulas.

• Energy Stored in a Capacitor: Direct formulas.

• Energy Density (u): Energy per unit volume.

• u = ½ ϵ₀E² (Energy is present where an electric field exists).

Current Electricity

The movement of charges through conductors forms the basis of everyday electrical systems. Concepts like current, resistance, and Ohm’s law, along with circuit rules such as Kirchhoff’s laws, are crucial for analyzing circuits and solving numerical problems efficiently.

• Current (I): Flow of charge.

• I = Q / t = ne / t

• Drift Velocity (v_d): Average velocity of charge carriers.

• v_d = eEτ / m

• Relation with current: I = neAv_d

• Resistance (R): Opposition to current flow.

• R = ρL / A = mL / (ne²τA)

• ρ (Resistivity): Specific resistance.

• Current Density (J): Current per unit cross-sectional area.

• J = I / A (A vector quantity).

• Conductivity (σ): σ = 1 / ρ

• Conductance (G): G = 1 / R

• Mobility (μ): Drift velocity per unit electric field.

• μ = v_d / E = eτ / m

• Effect of Temperature on Resistance:

• Conductors: Resistance increases with temperature.

• Semiconductors: Resistance decreases with temperature.

• Power (P): Rate of energy transfer.

• P = VI = I²R = V² / R

• Conditions of a Cell:

• Discharging: V = E - IR

• Charging: V = E + IR

• Short Circuiting: Terminal potential difference becomes zero.

• Isolated Cell: Terminal potential difference equals its EMF.

• Kirchhoff's Laws:

• First Law (Junction Rule): Conservation of Charge.

• Second Law (Loop Rule): Conservation of Energy.

• Combinations of Cells: Series and Parallel formulas.

• Wheatstone Bridge:

• Balanced Condition: No current flows through the galvanometer.

• Meter Bridge: R₁ / R₂ = (100 - L) / L

Magnetic Effects of Current

Electric currents generate magnetic fields, leading to important interactions between charges and magnets. Laws like Biot-Savart and Ampere’s law, along with the concept of Lorentz force, help explain these phenomena and are key to solving practical and conceptual problems.

• Biot-Savart Law: Used for magnetic field due to a current element.

• Magnetic Field due to Wires:

• Finite Wire: B = μ₀/4π (I/r) (sinφ₁ + sinφ₂)

• Infinite Length Wire: B = μ₀ / 2π (I / r)

• Magnetic Field due to Circular Loop:

• At Center: B = μ₀ NI / 2R

• Ampere's Circuital Law: Relates magnetic field to net current.

• ∮ B ⋅ dl = μ₀ I_net

• Magnetic Field Inside a Solenoid:

• B = μ₀nI (n = turns per unit length). At ends, field is half.

• Force on a Charge in Magnetic Field:

• F = qvB sinθ

• Lorentz Force: Total force on a charge in both electric and magnetic fields.

• F = qE + q(v × B)

• Force on a Current-Carrying Conductor in Magnetic Field:

• F = I L B sinθ

• Velocity Selector (Filter Circuit): v = E / B

• Force per Unit Length between Two Parallel Wires:

• F/L = μ₀ / 2π (I₁I₂ / R)

• Motion of a Charge in Magnetic Field:

• If θ = 0° or 180°: Straight line motion.

• If θ = 90°: Circular motion.

• If θ = General Angle: Helical path.

• Torque on a Current-Carrying Coil in Magnetic Field:

• τ = NIAB sinθ = MB sinθ

• Conversion of Galvanometer:

• Ammeter: Connect a shunt (low resistance) in parallel.

• Voltmeter: Connect a heavy resistance in series.

Electromagnetic Induction

Changing magnetic fields can produce electric current, forming the basis of many modern technologies. Principles like Faraday’s law and Lenz’s law explain how induced currents are generated, making these concepts essential for both theoretical understanding and numerical problem-solving.

• Magnetic Flux (Φ): Φ = BA cosθ

• Faraday's Law: Explains induced EMF.

• Induced Current: I = -N/R (ΔΦ / Δt)

• Motional EMF: Induced EMF when a conductor moves in a magnetic field.

• EMF = B L v

• Induced EMF in a Rotating Rod:

• If a rod rotates about its end: EMF = ½ BL²ω

• Self-Induction:

• NΦ = LI

• Self-Inductance of a Solenoid: L = μ₀n²A / l

• Mutual Inductance:

• NΦ_secondary = M I_primary

• Coefficient of Coupling (k): Represents flux linkage between coils.

• Combinations of Inductors:

• Series: L_eq = L₁ + L₂

• Parallel: L_eq = L₁L₂ / (L₁ + L₂)

Alternating Current (AC)

Electrical systems often use currents that vary with time rather than remain constant. Concepts like RMS values, impedance, phase difference, and resonance explain how AC circuits behave, which is important for solving real-world and exam-based circuit problems.

• Alternating Voltage: V = V₀ sin(ωt)

• Alternating Current: I = I₀ sin(ωt) (in purely resistive circuits).

• Average Value of AC:

• Full Cycle: Zero.

• Half Cycle: 2/π I₀

• RMS Value: I_rms = I₀ / √2

• Phase Relationship:

• Purely Resistive Circuit: Current and voltage are in the same phase.

• Purely Inductive Circuit: Voltage leads current by 90°.

• Purely Capacitive Circuit: Current leads voltage by 90°.

• Series LCR Circuit:

• Impedance (Z): Total effective resistance.

• Z = √(R² + (X_L - X_C)²)

• Phase Angle (φ): tan φ = (X_L - X_C) / R

• Condition of Resonance: X_L = X_C

• Power Dissipation: P = V_rms I_rms cosφ

• Efficiency = (Output Power / Input Power) × 100.

Ray Optics

Light can be understood through simple geometric principles like reflection and refraction. Mirrors, lenses, and optical instruments rely on these ideas, making this area highly scoring due to its predictable and formula-based questions.

• Reflection: Angle of incidence (i) = Angle of reflection (r).

• Mirror Formula: 1/f = 1/v + 1/u

• Focal Length: f = R / 2

• Refraction:

• Snell's Law: sin i / sin r = μ₂ / μ₁

• Critical Angle (θ_c): sin θ_c = 1 / μ_denser_to_rarer

• Refraction at Spherical Surfaces: μ₂ / v - μ₁ / u = (μ₂ - μ₁) / R

• Thin Lens Formula: 1/f = 1/v - 1/u

• Refraction through a Prism: sin((A + δ_m)/2) / sin(A/2) = μ

• Optical Instruments: Formulas for Simple Microscope, Compound Microscope, and Telescope are often questioned.

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Atoms

Atomic structure and energy levels explain how electrons behave within an atom. Models like Bohr’s theory and spectral series provide a clear framework for understanding atomic behavior and solving related numerical questions.

• Impact Parameter: Dependent on cot(θ/2).

• Distance of Closest Approach: This is very important for frequently asked questions.

• Bohr's Quantization Condition: mvr = n(h / 2π)

• Formulas for: Speed of Electron, Radius, Kinetic Energy, Potential Energy, Total Energy.

• Hydrogen Spectrum: Series include Lyman, Balmer, Paschen, Bracket, Pfund.

• Rydberg's Constant (R_H) value should be known.

• For Maximum Wavelength: Use minimum n value.

• For Minimum Wavelength: Use infinite n value.

Nuclei

The structure of the nucleus, along with concepts like binding energy and radioactivity, explains nuclear stability and reactions. These ideas are important for direct formula-based questions and understanding fundamental nuclear processes.

• Radius of Nucleus: R = R₀ A^(1/3)

• R₀ = 1.2 fm (10⁻¹⁵ m).

• Density of Nucleus: In the range of 10¹⁷ kg/m³.

• Atomic Mass Unit (AMU): 1 amu = 1.66 × 10⁻²⁷ kg.

• Mass Defect (Δm):

• Δm = (Mass of protons + Mass of neutrons) - Mass of nucleus.

• Binding Energy (BE):

• If mass is in kg: BE = Δm × c².

• If mass is in amu: BE = Δm × 931 MeV.

• Energy of Reaction (Q-value): Specific formula available.

Semiconductors

Modern electronics rely on materials whose conductivity can be controlled. Concepts like intrinsic and extrinsic semiconductors, diodes, and transistors explain how electronic devices function, making this area important for both theory and application.

• Intrinsic Carrier Concentration: n_i² = n_e × n_h (Intrinsic carrier concentration squared equals electron concentration times hole concentration).

• Formulas for Conductivity and Resistivity in Semiconductors.

• Half-wave and Full-wave Rectifiers: Formulas for current values should be known.

Strong command over physics formulas across all topics is essential for CUET success, as the exam prioritizes speed and accuracy. Organising concepts chapter-wise and revising them regularly improves recall and problem-solving efficiency, helping students handle diverse question types with confidence and maximise their overall score.

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