Is it true that Electric current flows from negative to positive terminals.?

Conventional current flows from positive to negative, while electron flow (actual charge movement) is from negative to positive.

Is it true that A magnetic field can do work on a moving charge.?

The magnetic force is always perpendicular to the velocity, so it changes the direction of motion but not the kinetic energy or speed of the charge.

Class 12 Physics Formula Cheatsheet

This cheatsheet provides essential formulas and concepts for Class 12 Physics, covering Electric Charges and Fields, Potential and Capacitance, Current Electricity, Moving Charges and Magnetism, and Ray Optics. It is designed for quick revision based on NCERT syllabi.

Core Principles

Electric Field (E) and Potential (V) are derived from charge distribution, with E = -∇V and V = W/q.
Capacitance (C) relates charge (Q) and voltage (V) as C = Q/V, with energy stored as U = CV²/2.
Current (I) is the flow of charge (I = dQ/dt), governed by Ohm's Law (V=IR) and related to current density (J=I/A) and conductivity (σ).
Magnetic fields (B) exert forces (Lorentz force F = q(E + v x B)) on moving charges and are generated by currents (Biot-Savart Law, Ampere's Law).
Ray optics uses lens and mirror formulas (1/f = 1/v + 1/u for mirrors, 1/f = 1/v - 1/u for lenses) and magnification (m = -v/u) to describe image formation.

Action Steps

1. Identify the type of charge distribution (point charge, dipole, line, sheet, shell) to select the appropriate electric field and potential formulas.
2. Apply vector addition for forces and fields when multiple charges are present.
3. Use Gauss's Law to simplify electric field calculations for symmetric charge distributions.
4. Calculate capacitance using C=Q/V and determine the equivalent capacitance for series (1/Ceq = Σ 1/Ci) and parallel (Ceq = Σ Ci) combinations.
5. Apply Ohm's Law (V=IR) and Kirchhoff's rules (junction and loop) to analyze current and voltage in circuits.
6. Use the Lorentz force equation to find the force on a charge in electric and magnetic fields.
7. Apply Biot-Savart or Ampere's Law to find magnetic fields due to current distributions.
8. Use mirror (1/f = 1/v + 1/u) and lens (1/f = 1/v - 1/u) formulas, paying close attention to sign conventions, to determine image characteristics.
9. Calculate magnification (m = -v/u) for mirrors and lenses to find the size and orientation of the image.

Formulas

Coulomb's Law: $F = k|q_1q_2|/r^2$
Electric Field of a point charge: $E = kq/r^2$
Electric Field of a dipole (far field): $E_{axial} = 2kp/r^3$, $E_{equatorial} = kp/r^3$
Gauss's Law: $\oint \vec{E} \cdot d\vec{A} = Q_{enc}/\epsilon_0$
Electric Potential of a point charge: $V = kq/r$
Capacitance: $C = Q/V$
Energy stored in a capacitor: $U = CV^2/2 = QV/2 = Q^2/(2C)$
Current: $I = dQ/dt$
Drift velocity: $v_d = eEt/m$
Ohm's Law: $V = IR$
Current Density: $J = I/A = \sigma E$
Resistance: $R = \rho L/A$
Power: $P = VI = I^2R = V^2/R$
Lorentz Force: $"F = q(\vec{E} + \vec{v} \times \vec{B})$
Magnetic field due to a long wire: $B = \mu_0 I / (2\pi r)$
Magnetic field at the center of a circular loop: $B = \mu_0 NI / (2R)$
Force on a current-carrying wire: $"F = I("L \times \

Key Terms

Electric Flux (Φ): Measure of the electric field passing through a given surface area, calculated as Φ = EAcosθ.
Equipotential Surface: A surface where the electric potential is constant; no work is done moving a charge along it.
Current Density (J): Current per unit cross-sectional area, J = I/A, and related to the electric field by J = σE.
Lorentz Force: The total force experienced by a charged particle moving in electric and magnetic fields: F = q(E + v × B).
Total Internal Reflection (TIR): Occurs when light travels from a denser to a rarer medium at an angle of incidence greater than the critical angle (sin C = n₂/n₁).

Pro Tips

When dealing with dielectrics in capacitors, note that battery OFF means Q and V are fixed, while battery ON means V and E are fixed.
For moving charges in magnetic fields, remember that the magnetic force (F = qvBsinθ) does no work because it's always perpendicular to velocity.
In ray optics, consistently use the sign convention: light travels left to right, object distance (u) is negative for real objects, and focal length (f) is negative for concave mirrors/diverging lenses.

Pitfalls to Avoid

Confusing electric field (vector) with electric potential (scalar) leads to incorrect calculations.
Ignoring sign conventions in mirror and lens formulas results in wrong image locations and types.
Applying formulas for infinite charge distributions to finite ones causes significant errors.

Myth vs Reality

Electric current flows from negative to positive terminals.: Conventional current flows from positive to negative, while electron flow (actual charge movement) is from negative to positive.
A magnetic field can do work on a moving charge.: The magnetic force is always perpendicular to the velocity, so it changes the direction of motion but not the kinetic energy or speed of the charge.

Real World Examples

A parallel plate capacitor filled with a dielectric.: When the dielectric is inserted with the battery OFF, charge (Q) and voltage (V) remain constant, but capacitance (C) increases by a factor of K, and energy density (u) decreases if V is fixed.
A charged particle moving in a uniform magnetic field.: The particle undergoes circular motion if velocity is perpendicular to the field (r = mv/(|q|B)) or helical motion if there's a parallel velocity component (pitch p = vcosθ T).

Statistics

Elementary charge (e): 1.602 × 10⁻¹⁹ C
Coulomb's constant (k): ≈ 9 × 10⁹ Nm²/C²
Permeability of free space (μ₀): 4π × 10⁻⁷ H/m
Near point for distinct vision (D): 25 cm

Timeline

1785: Charles-Augustin de Coulomb publishes his law of electrostatic force between charges.
1820: Hans Christian Ørsted discovers that electric currents create magnetic fields; André-Marie Ampère formulates the law relating current and magnetic field.
1831: Michael Faraday discovers electromagnetic induction, the principle behind generators and transformers.
1873: James Clerk Maxwell unifies electricity and magnetism with his equations, predicting electromagnetic waves.
1888: Heinrich Hertz experimentally confirms Maxwell's predictions of electromagnetic waves.

People

Charles-Augustin de Coulomb: Formulated the law of electrostatic force.
Gauss: Developed Gauss's Law relating electric flux to enclosed charge.
Ohm: Formulated Ohm's Law relating voltage, current, and resistance.
Biot and Savart: Developed the law for calculating magnetic fields from current elements.
Ampère: Formulated Ampere's Law relating magnetic fields to electric currents.
Maxwell: Unified electricity and magnetism with his equations.

Quiz

What is the unit of electric potential?: Volt
If two resistors are connected in series, the current through them is:: The same
Which phenomenon is responsible for the formation of rainbows?: Dispersion