Electrostatics

Electrostatics

When a glass rod is rubbed with silk, this acquires power to attract light bodies such as small pieces of paper. The bodies which acquire this power are said to be charged. If these charges do not move they are called static charges and the branch of physics which deals with static charges is called electrostatics.

• COULOMB'S LAW
  The magnitude of the force (F) of attraction or repulsion between two point charges and placed in vacuum at separation r is
  a) directly proportional to the product of the magnitude of the two charges.
  F q₁q₂ ...(i)
  b) inversely proportional to the square of the distance of separation between them.
  F ...(ii)
  In vector forms
  Note : When two identical bodies having charges q₁ and q₂ respectively are brought in contact and separated, then the charge on each body
  is .
  
• ELECTROSTATIC FIELD
  The region of space around a source charge (q) in which it can exert a force on a test charge (q₀). Mathematically, electric field is the force experienced per unit test charge q₀ placed in the electrostatic influence of source charge q .
  , where q₀ 0
  Electric field strength is a vector quantity directed away from a positive charge and towards the negative charge. SI unit of electric field is newton/coulomb or .
  The dimensional formula for is [] .
• ELECTRIC FLUX
  The mathematical quantity related to number of lines passing through a surface is called the electric flux . The electric flux through a surface which is perpendicular to a uniform electric field E is defined as the product of electric field E and surface area A :
  Since the electric field is proportional to density of lines of force, the electric flux is proportional to number of lines of force passing through the surface area : .
  If the surface area is not perpendicular to the electric field, then the electric flux is given by
  
  Where is a unit vector perpendicular to the surface and is the component of electric field perpendicular to the surface (normal component).
  
• GAUSS LAW STATEMENT
  
  where qenclosedis the total charge enclosed inside the surface. This important result is called Gauss's Law and can be stated as follows:
  
  For a system of charges, the net flux through any closed surface 'S' is equal to times the net charge inside the surface.
  
• ELECTRIC PPOTENTIAL
  Electric potential and potential energy are defined only for conservative fields.
  Definition in terms of work done :
  Potential at any point A is equal to the amount of work done (by external agent against electric field) in bringing a unit positive charge from infinity to that point.
  
  Unit of potential (V) = J/C or volt.
  Since work and charge, both are scalars, the electric potential is a scalar quantity.
  
  The dimensions of electric potential are
  
  or [V] = ML²T^-3A^-1
• POTENTIAL DIFFERENCE
  Potential difference between two points f (final) and i (initial) is defined to be equal to the amount of work done (by external agent) in moving a unit positive charge from point i (initial) to f (final)
  
  
  
  If work done in carrying a unit positive charge from point 1 to point 2 is one joule then the potential difference V₂ - V₁ is said to be one volt.
  Potential difference may be positive or negative.
• RELATION BETWEEN E AND ELECTRIC POTENTIAL V
  V = V_f - V_i =
  
  In one dimensions
  ......(1)
  
  ........(2)
  Note : In an extended region of space where electric field is zero, electrical potential is constant
  
  
  .
• ELECTRIC DIPOLE
  An arrangement of two equal and opposite charges separated by a small distance is called an electric dipole.
  
  The dipole moment is a vector quantity whose magnitude is equal to the product of magnitude of one charge and the distance between the two charges. It is directed from negative charge to positive charge.
  
  Unit of dipole moment (p) = coulomb × metre = C.m
  Dimensions of p = M₀L₁T₁A₁
• FORCE AND TORQUE ON A DIPOLE PLACED IN AN ELECTRIC FIELD
  (a) A positive charge +q experiences a force parallel to the electric field
  (b) A negative charge -q experiences a force in a direction opposite to that of the electric field
  
  
  
  (c) The total force on a dipole placed in an uniform electric field is zero = 0
  (d) The torque on a dipole placed in uniform electric field is
  
  
• CHARGED LIQUID DROP
  If n small drops each of radius r coalesce to form a big drop of radius R, then
  
  (i)
  
  R = rn_1/3
  (ii) If each small drop has a charge q, then the charge on the big drop
  
  (iii) If V is the potential of the small drop, then the potential of the big drop will be
  
  
  
• FORCE ON A CHARGED SURFACE
  (i) If we consider an element of the charged surface, then the charge on the element experiences a repulsive force due to the charge on the remaining part. As a result, a resultant force acts on it perpendicular to the surface in the outward direction.
  (iii) If s is the surface charge density, then the electric field intensity at external points close to the surface is and at internal points close to the surface the field is zero. Thus the average intensity at the surface
  
  
  
  (iv) The repulsive force acting on a unit area of the surface will be.
  
  N/m2
  
  (v) The repulsive force acts in the outwards direction. The force acting on a unit area of the surface is electrical pressure.
  
  = 2pKs2 N/m2
  
  
• MOTION OF A CHARGED PARTICLE IN ELECTRIC FIELD
  
  (i) A charged particle at rest or moving experiences a force in the presence of electric field. The acceleration, velocity and displacement
  are given by
  
  
  
  
  
  
  
  (ii) For a charged particle with initial velocity perpendicular to the electric field
  Note that F_x = 0, a_x = 0, V_x = u at all times
  
  Fy = qE, ay = , Vy = t
  The displacement components are x = ut
  
  
  Eliminating t, which is the equation of a parabola.
  
  
• ELECTROSTATIC SHIELDING
  If there is a cavity of any shape inside a conductor, the field there will be strictly zero. This property is called electrostatic shielding because any thing placed inside the cavity will be completely shielded from external fields.
  
  1. Non-polar dielectrics :
  In the presence of an external field, the two centres of electrons and protons get slightly separated and each molecule becomes a dipole, having a small dipole moment.
  
  2. Polar Dielectrics : In polar dielectrics the centre of mass of the protons in a molecule do not coincide with the centre of mass of the electrons.
  
  a) Dielectric Constant is the ratio of applied field to field induced in dielectric i.e.
  
  
  b) Dielectric Strength : The dielectric strength of a dielectric is the maximum value of the electric field that can be applied to the dielectric without its electric breakdown, i.e., without liberating electrons from its atoms (or molecules).
• Capacitors are the mechanism to store charges, hence store electrostatic energy. A simple parallel plate capacitor has a capacity as
  
  Where A = area of plate
  d = distance between plates
  e_r = permittivity of any medium between plates
  
  In series combination
  
  In parallel combination C_eq = C₁+C₂+C₃.................