Electrostatics, electric fields and capacitors
Charge is a conserved property
Electrostatics examines charges and their interactions when a steady charge distribution is a useful approximation. Ordinary matter contains positively charged protons and negatively charged electrons. An object becomes negatively charged when it gains electrons and positively charged when it loses electrons. Rubbing does not create charge from nothing: it can transfer electrons between materials. In an isolated system the total electric charge is conserved. Charge is measured in coulombs, C. The elementary charge magnitude is approximately 1.60 × 10⁻¹⁹ C, so macroscopic charges represent very large numbers of elementary charges. Protons ordinarily remain within nuclei during everyday charging processes.
Conductors, insulators and induction
In a conductor, mobile charge carriers can redistribute through the material; in a solid metal these are electrons. An insulator restricts that movement, although it can still become polarised. Bringing a charged object near a neutral object can separate its positive and negative charge effects without transferring net charge to it. This explains why attraction does not alone prove that two objects carry opposite net charges. A charged object can attract a neutral polarised object. Repulsion between two initially isolated objects is stronger evidence that they carry like net charges. Distinguish redistribution, transfer by contact and transfer through a grounded connection.
Reasoning about an electroscope
An electroscope responds when charge redistribution or transfer causes its movable parts to repel. Its behaviour depends on its initial charge and the sequence of operations. A nearby charged rod may change leaf divergence without touching the instrument. Removing the rod can reverse that change if no net charge has been exchanged. In charging by induction, grounding and the order of disconnecting matter because they determine whether charge can enter or leave. Draw the charge distribution at each stage instead of memorising that every approaching rod must increase divergence. The same observation can have different explanations under different initial conditions.
Coulomb and proportional reasoning
For two small stationary charges separated by distance r in air or vacuum, the magnitude is, with k approximately 9.0 × 10⁹ N m² C⁻². It acts along their joining line, attracting unlike charges and repelling like charges. Double one charge and the doubles; double the separation and the becomes one quarter. Convert microcoulombs to 10⁻⁶ C before substitution. The point-charge model is appropriate when object sizes and redistribution effects do not undermine the approximation. In another medium, the electrical properties of the medium change the interaction, so do not reuse the vacuum constant without considering the stated model.
Electric field has direction
Electric field strength is per unit positive test charge. Its unit is N/C, also expressible as V/m. Field arrows point away from a positive source and towards a negative source. A positive test charge experiences in the field direction; a negative charge experiences in the opposite direction. For a point source, gives magnitude. Fields combine as vectors. At a midpoint between equal like charges, their fields can cancel, while the potentials add. Between equal opposite charges, the fields reinforce along the line rather than cancelling.
Potential is not field strength
Electric potential is potential per unit charge, measured in volts or joules per coulomb. Potential difference describes transfer per unit charge between two positions. For a point source with zero potential chosen at infinity, includes the sign of Q. Potential is a scalar, so contributions add algebraically. Work and changes use. A negative value means the system's potential decreases for that . Do not replace the charge by its magnitude when the sign determines the physical meaning. A high potential does not by itself specify field strength, which depends on spatial change in potential.
Uniform fields and conductors
Between large parallel plates away from their edges, a uniform field is a useful approximation, with magnitude. The field points from higher to lower potential. A plate spacing of 0.004 m with a 12 V difference gives 3,000 V/m, not 3 V/m. In electrostatic , the field inside the conducting material is zero and a connected conductor is at one potential. These statements concern a settled electrostatic situation. They do not that a -carrying wire has no electrical transfer or that every cavity and external region has identical fields.
Capacitance connects charge and
A capacitor stores separated charge and in an electric field. Its capacitance is, where Q is the magnitude of charge on either plate and V the potential difference. The plates carry equal and opposite charges in the simple two-plate model, so the capacitor need not have a net charge. The farad is large; microfarads and nanofarads are common exercise units. For an ideal parallel-plate capacitor. Larger overlapping area increases capacitance, larger separation reduces it, and an appropriate dielectric changes the permittivity ε. Geometry and material determine capacitance in this ideal model, not the stored charge alone.
Combining capacitors correctly
Capacitors in parallel share a potential difference, and their charges add: Ctotal = C₁ + C₂ + …. Capacitors in a simple series chain have equal charge magnitudes on each capacitor, while their potential differences add. Thus two positive capacitances in series produce an equivalent smaller than either, a useful arithmetic check. For 2 µF and 3 µF, the parallel total is 5 µF and the series total is 1.2 µF. This is the opposite numerical pattern from resistor combinations. Redraw the nodes before choosing a formula; physical placement on a page does not determine electrical connection.
Stored and changing conditions
A capacitor stores . Convert both capacitance and to consistent units. A 6 µF capacitor at 12 V holds 72 µC and stores 4.32 × 10⁻⁴ J. If a capacitor remains connected to an ideal source, its is held constant when its geometry changes. If isolated with negligible leakage, its charge is held constant instead. These are different conditions and lead to different changes. A dielectric can increase capacitance, but the effect on and depends on whether the source remains connected.
Applications and assessment method
Capacitors support timing, smoothing and temporary storage; an ideal capacitor does not sustain a steady conduction through its dielectric after charging in a DC circuit. Real components have leakage, limits and other nonideal behaviour. Stored can remain after a is disconnected, so this lesson is calculation and interpretation, not a guide to opening electrical equipment. In an examination, state the model, draw signs and directions, convert prefixes, select the equation and check the result's unit and size. For written explanations, distinguish charge, , field, potential, capacitance and explicitly rather than calling all of them electricity.