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

Conventional current is defined as the flow of positive charge from higher potential (positive) to lower potential (negative), even though in metals, it's the electrons (negative charge) that actually move from lower to higher potential.

Is it true that A magnetic field exerts a force on a stationary charge.?

The magnetic force on a charge is given by F = q(v × B). If the charge is stationary (v=0), the magnetic force is zero, regardless of the magnetic field strength.

Class 12 Physics Formula Cheatsheet

This cheatsheet condenses essential physics formulas and concepts for Class 12 NCERT syllabi, covering electric charges, fields, potential, capacitance, current electricity, moving charges, magnetism, and ray optics.

Core Principles

Electric Fields & Charges: Governed by Coulomb's Law (F=kq₁q₂/r²) and Gauss's Law (∮E·dA = Qenc/ε₀), with fields from point charges (E=kq/r²) and dipoles (E=2kp/r³).
Potential & Capacitance: Potential (V=kq/r) is algebraic sum; capacitance (C=Q/V) relates charge and voltage, with series (1/Ceq=Σ1/C) and parallel (Ceq=ΣC) combinations.
Current Electricity: Current (I=dQ/dt) is flow of charge; Ohm's Law (V=IR) relates voltage, current, and resistance; power (P=VI) and energy (W=Pt) are key.
Moving Charges & Magnetism: Lorentz force (F=q(E+v×B)) acts on charges in fields; magnetic fields are generated by currents (Biot-Savart, Ampere's Law); forces on wires (F=BILsinθ) and circular motion (r=mv/|q|B) are fundamental.
Ray Optics: Governed by mirror (1/f=1/v+1/u) and lens (1/f=1/v-1/u) formulas, magnification (m=h₁/h₀=-v/u), and principles like refraction (n₁sin i=n₂sin r) and total internal reflection (sin C=n₂/n₁).

Action Steps

1. Identify the charge configuration (point, dipole, sheet, shell) to select the correct electric field and potential formulas.
2. Apply vector addition for forces and fields when multiple charges are present.
3. Use Gauss's Law for symmetric charge distributions to simplify flux calculations.
4. Sum potentials algebraically for multiple sources; remember potential is a scalar.
5. Analyze series and parallel combinations for resistors and capacitors to find equivalent values.
6. Apply Ohm's Law (V=IR) and power formulas (P=VI) to solve circuit problems.
7. Use the Lorentz force equation to determine the force on a charge in combined electric and magnetic fields.
8. Apply the Biot-Savart Law or Ampere's Law to find magnetic fields due to current distributions.
9. Use the mirror and lens formulas with proper sign conventions to find image positions and characteristics.
10. Apply the law of refraction (Snell's Law) and the concept of critical angle for total internal reflection.

Formulas

Coulomb's Law: $F = k\frac{|q_1q_2|}{r^2}$
Electric Field (Point Charge): $E = k\frac{q}{r^2}$
Electric Field (Dipole, Axial): $E_{axial} = \frac{2kp}{r^3}$
Electric Field (Dipole, Equatorial): $E_{equatorial} = \frac{kp}{r^3}$
Gauss's Law: $\oint \vec{E} \cdot d\vec{A} = \frac{Q_{enc}}{\varepsilon_0}$
Potential (Point Charge): $V = k\frac{q}{r}$
Capacitance: $C = \frac{Q}{V}$
Capacitance (Parallel Plate): $C = \frac{\varepsilon_0 A}{d}$
Capacitance (Dielectric): $C = K \frac{\varepsilon_0 A}{d}$
Energy Stored in Capacitor: $U = \frac{1}{2}CV^2 = \frac{1}{2}\frac{Q^2}{C} = \frac{1}{2}QV$
Current: $I = \frac{dQ}{dt}$
Drift Velocity: $v_d = \frac{eEt}{m}$
Current Density: $J = \sigma E$
Ohm's Law: $V = IR$
Resistance: $R = \rho \frac{L}{A}$
Power: $P = VI = I^2R = \frac{V^2}{R}$
Heating Effect: $H = I^2Rt$
Lorentz Force: $\\vec{F} = q(\vec{E} + \vec{v} \times \vec{B})$
Magnetic Force on Wire: $F = ILB\sin\theta$
Circular Motion in Magnetic Field: $r = \frac{mv}{|q|B}$
Biot-Savart Law: $d\vec{B} = \frac{\mu_0 I(d\vec{l} \times \hat{r})}{4\pi r^2}$
Magnetic Field (Long Wire): $B = \frac{\mu_0 I}{2\pi r}$
Mirror Formula: $\\frac{1}{f} = \frac{1}{v} + \frac{1}{u}$
Lens Formula: $\\frac{1}{f} = \frac{1}{v} - \frac{1}{u}$
Magnification: $m = \frac{h_i}{h_0} = -\frac{v}{u}$
Refraction: $n_1\sin i = n_2\sin r$
Critical Angle: $\\sin C = \frac{n_2}{n_1}$

Key Terms

Electric Field (E): The force per unit charge experienced by a test charge at a point in space, measured in N/C or V/m.
Electric Potential (V): The work done per unit charge to move a test charge from infinity to a point in an electric field, measured in Volts (J/C).
Capacitance (C): The ratio of charge stored on a conductor to the potential difference across it (C=Q/V), measured in Farads (C/V).
Current Density (J): The electric current per unit area flowing through a conductor (J=I/A), measured in A/m².
Lorentz Force: The total force experienced by a charged particle moving in both electric and magnetic fields: F = q(E + v × B).
Biot-Savart Law: Describes the magnetic field generated by a small segment of current-carrying wire.
Total Internal Reflection (TIR): The phenomenon where light traveling from a denser to a rarer medium is completely reflected back into the denser medium when the angle of incidence exceeds the critical angle.

Pro Tips

For dipoles, remember the field strength decreases as 1/r³ (much faster than a point charge's 1/r²).
Equipotential surfaces are always normal to the electric field lines.
When a dielectric is inserted into a capacitor with the battery ON, voltage and field remain constant, while charge and energy increase by factor K.
When a dielectric is inserted with the battery OFF, charge and field remain constant, while voltage and energy decrease by factor K.
The magnetic part of the Lorentz force (q v × B) does no work because it's always perpendicular to the velocity.
For ray optics, consistently use the sign conventions: real is positive, virtual is negative; light travels left to right; distances measured from the pole/optical center.
A galvanometer's sensitivity can be increased by increasing the magnetic field (B), number of turns (N), or area (A), or decreasing the spring constant (C).

Pitfalls to Avoid

Confusing scalar potential (V) with vector field (E); potential is algebraic sum, field is vector sum.
Incorrectly applying sign conventions in mirror and lens formulas, leading to wrong image locations or types.
Forgetting that the magnetic force on a moving charge does no work, meaning kinetic energy and speed remain constant in a purely magnetic field.
Assuming a uniform electric field when dealing with point charges or dipoles; fields vary with distance.
Mixing up series and parallel formulas for resistors and capacitors; ensure correct application based on how components are connected.

Myth vs Reality

Electric current flows from negative to positive.: Conventional current is defined as the flow of positive charge from higher potential (positive) to lower potential (negative), even though in metals, it's the electrons (negative charge) that actually move from lower to higher potential.
A magnetic field exerts a force on a stationary charge.: The magnetic force on a charge is given by F = q(v × B). If the charge is stationary (v=0), the magnetic force is zero, regardless of the magnetic field strength.

Real World Examples

A parallel plate capacitor with plate area A and separation d.: Its capacitance is C = ε₀A/d, which increases if a dielectric material (K>1) is inserted or if the plate separation decreases.
An electron moving in a uniform magnetic field.: It undergoes uniform circular motion if its velocity is perpendicular to the field, with radius r = mv/(|q|B), because the magnetic force provides the centripetal force.
Light traveling from water (n≈1.33) to air (n≈1.00).: Total internal reflection occurs if the angle of incidence in water exceeds the critical angle C, where sin C = 1/1.33 ≈ 0.75, so C ≈ 48.75°.

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
Microscope Magnification (near point): M ≈ (L/f_obj)(1 + D/f_eye)
Telescope Magnification (normal adjustment): M = -f_obj / f_eye

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 laws relating electricity and magnetism.
1831: Michael Faraday discovers electromagnetic induction, the principle behind generators and transformers.
1873: James Clerk Maxwell unifies electricity, magnetism, and light in his theory of electromagnetism.
1888: Heinrich Hertz experimentally confirms Maxwell's predictions of electromagnetic waves.

People

Charles-Augustin de Coulomb: Formulated the law of electrostatic force between electric charges.
André-Marie Ampère: Developed laws describing the magnetic effects of electric currents.
Michael Faraday: Pioneered work on electromagnetism and induction.
James Clerk Maxwell: Unified electricity, magnetism, and light into a single theory.
Christiaan Huygens: Proposed a wave theory of light, relevant to ray optics principles.

Quiz

What is the unit of electric field strength?: Both A and B
If a dielectric material with K=2 is inserted into a capacitor with the battery disconnected (OFF), what happens to the charge Q?: Q remains the same
What type of image is formed by a convex mirror?: Virtual, erect, and diminished