May 2011 - Career Point

PHYSICS FUNDAMENTAL FOR IIT-JEEElectrostatics-IKEY CONCEPTS & PROBLEM SOLVING STRATEGY• Coulomb's Law :1 q1q2F 0 =(in vacuum)24πε0 rVectorially → 1 q1q2F = rˆ24πε0 r1 q1q2In any material medium F =24πε0εrrwhere ε r is a constant of the material medium calledits relative permittivity, and ε 0 is a universal constant,called the permittivity of free space.ε 0 = 8.85 × 10 –12 1or4πε = 9 × 1090The unit of ε 0 is C 2 N m –2 or farad per metre.1 q1q2Also F =24πε0εrrWhere ε is called the absolute permittivity of themedium.Obviously, ε r = F 0 /F. Remember ε r = ∞ forconductors.Conductors and insulators Each body containsenormous amounts of equal and opposite charges. A'charged' body contains an excess of either positive ornegative charge.In a conductor, some of the negative charges are freeto move around. In an insulator (also called adielectric), the charges cannot move. They can onlyundergto small localized displacements, causingpolarization.Induction When a charged body A is brought nearanother body B, unlike charges are induced on thenear surface of B (called bound charges) and likecharges appear on the far surface of B (called freecharges) If B is a conductor, the free charges can beremoved by earthing B, e.g., by touching it. If B is aninsulator, separation of like and unlike charges willstill occur due to induction. However, the likecharges cannot then be removed by earthing B.• Electric Field And PotentialElectric Field An electric field of strength E is saidto exist at a point if a test charge ∆q at that pointexperiences a force given by→→ →→∆ F∆ F = ∆qF or E =∆qThe unit of electric field is Newton per coulomb orvolt per metre. The electric field strength at adistance r from a point charge q in a medium ofpermittivity ε is given byE =14πεq2rVectorially → 1 qE = 4πε2 rˆrWith reference to any origin→E =q4πε→R−r→→3→R−rWhere R → is the position vector of the field point and→r , the position vector of q.Due to a number of discrete chargesi=N→→→q E =1 R−ri∑34πε→ →i=1R−riElectric Potential The electric potential at a point isthe work done by an external agent in bringing a unitpositive charge from infinity up to that point alongany arbitrary path.∆W∞→(by an external agent)V P = Pvolt(V) or JC –1∆qThe potential difference between two points P and Qis given by∆W Q → P (by agent)V P – V Q =volt (V)∆qThe potential at a distance r from a point charge q ina medium of permittivity ε isϕ or V =14πεq 1 =r 4πεq→ →R− rwith reference to any arbitrary origin.Due to a number of chargesi=N1 q1ϕ or V = ∑4πε→ →i= 1 R−riXtraEdge for IIT-JEE 20 MAY 2011