ELECTRIC CHARGES AND FIELDS 2ND PUC PHYSICS
Electric charges :
- Electric charges are of two types
- Positive charges and negative charges
- Like charges repel and unlike charges attract.
- By convention, the charge on a glass rod rubbed with silk is positive; that on a plastic rod rubbed with fur is then negative.
Conductors and insulators:
- Conductors allow movement of electric charge through them, insulators do not.
- In metals, the mobile charges are electrons; in electrolytes both positive and negative ions are mobile.
Electric charge has three basic properties:
- Quantization: Quantization of electric charge means that total charge (q) of a body is always an integral multiple of a basic quantum of charge (e) i.e., q = n e, where n = 0, ±1, ±2, ±3 … Proton and electron have charges +e, –e, respectively.
- Additivity: Additivity of electric charges means that the total charge of a system is the algebraic sum (i.e., the sum taking into account proper signs) of all individual charges in the system.
- Conservation: conservation of electric charges means that the total charge of an isolated system remains unchanged with time i.e. charge can neither be created nor destroyed.
Coulomb’s Law:
The mutual electrostatic force between two point charges q1 and q2 is proportional to the product q1 q2 and inversely proportional to the square of the distance r21 separating them.
- Mathematically,
F21 = force on q2 due to
where ȓ21 is a unit vector in the direction from q1 to q2 and k = 1/ 4πε is the constant of proportionality. - In SI units, the unit of charge is coulomb.
- The experimental value of the constant is ε0 = 8.854 × 10–12 C2 N–1 m–2
- The approximate value of k is k = 9 × 109 N m2 C–2
- The ratio of electric force and gravitational force between a proton and an electron is
Superposition Principle:
The principle is based on the property that the forces with which two charges attract or repel each other are not affected by the presence of a third (or more) additional charge(s).
Electric field line:
An electric field line is a curve drawn in such a way that the tangent at each point on the curve gives the direction of electric field at that point. The relative closeness of field lines indicates the relative strength of electric field at different points; they crowd near each other in regions of strong electric field and are far apart where the electric field is weak. In regions of constant electric field, the field lines are uniformly spaced parallel straight lines.
- Some of the important properties of field lines are:
- Field lines are continuous curves without any breaks.
- Two field lines cannot cross each other.
- Electrostatic field lines start at positive charges and end at negative charges —they cannot form closed loops.
In a uniform electric field E, a dipole experiences a torque given by = p × E but experiences no net force.
The flux ∆φ of electric field E through a small area element ∆S is given by
∆φ = E.∆S
The vector area element ∆S is ∆S = ∆S. n̂ where ∆S is the magnitude of the area element and n̂ is normal to the area element.
∆φ = E.∆S
The vector area element ∆S is ∆S = ∆S. n̂ where ∆S is the magnitude of the area element and n̂ is normal to the area element.
Gauss’s law:
The flux of electric field through any closed surface S is 1/εo times the total charge enclosed by S. The law is useful in determining electric field E, when the source distribution has simple symmetry:
Where r is the perpendicular distance of the point from the wire and is the radial unit vector in the plane normal to the wire passing through the point.
Here n̂ is a unit vector normal to the plane, outward on either side.
Where r is the distance of the point from the centre of the shell and R the radius of the shell. q is the total charge of the shell: q = 4πR2σ. The electric field outside the shell is as though the total charge is concentrated at the centre. The same result is true for a solid sphere of uniform volume charge density. The field is zero at all points inside the shell.
- Thin infinitely long straight wire of uniform linear charge density
Where r is the perpendicular distance of the point from the wire and is the radial unit vector in the plane normal to the wire passing through the point.
- Infinite thin plane sheet of uniform surface charge density σ
Here n̂ is a unit vector normal to the plane, outward on either side.
- Thin spherical shell of uniform surface charge density σ
Where r is the distance of the point from the centre of the shell and R the radius of the shell. q is the total charge of the shell: q = 4πR2σ. The electric field outside the shell is as though the total charge is concentrated at the centre. The same result is true for a solid sphere of uniform volume charge density. The field is zero at all points inside the shell. 2nd PUC Physics Electric Charges and Fields List of Topics
| Introduction to Electric Charges | Electric charges |
| Conductors and insulators | |
| Charging by induction | |
| Basic properties of electric charge | Additivity of charges |
| Charge is conserved | |
| Quantisation of charges | |
| Coulomb’s law | Statement |
| Derivation | |
| Forces between multiple charges | Superposition principle |
| Electric field | Electric field due to a system of charges |
| Physical significance of electric field | |
| Electric field lines | Properties and representation |
| Electric flux | Area element vector |
| Electric flux through an area element | |
| Electric dipole | The field of an electric dipole |
| Physical significance of dipoles | |
| Dipole in a uniform external field | |
| Continuous charge distribution | Definition of surface |
| Linear and volume charge densities | |
| Electric field due to continuous charge distribution | |
| Gauss’s Law | Statement |
| Derivation | |
| Applications of Gauss law | Field due to uniformly charged: a) Infinitely long straight wire b) Infinitely plane sheet c) Thin spherical shell |
| Numericals | Concept based problems |