Tiêu đề 01. ELECTRIC CHARGES and FIELDS.pdf ✅

Electrostatics deals with the study of forces, fields and potentials arising from static charges Electric Charge- It is the basic physical property of matter and due to this property, a force is experienced when kept in the field of electricity. Electric charges are of two types, 1. Positive Charge Lesser number of electrons than a number of protons Positive charges or protons have a charge of +1.6 × 10-19 Coulomb. A positive charge has its field lines emerging from within and going up to infinity 2. Negative Charge More number of electrons than number of protons Negative charges or Electrons have a charge of -1.6 × 10-19 Coulomb. A Negative charge has its field lines coming from infinity. The above example where hair strands start to attract to the ruler is due to electric charges. Similarly, rubbing a balloon on hair attracts hair to the balloon, in case two balloons are simultaneously rubbed, the balloons will start to repel each other, but they will attract the hair strands. The rate of change of electric charge is known as Electric current, I = q/t Conductors and Insulators Conductors- Conductors are the materials or substances which allow electricity to flow through them. They conduct electricity because they allow electrons to flow easily inside them from atom to atom. Also, conductors allow the transmission of heat or light from one source to another. Metals, humans, earth, and animals are all conductors. This is the reason we get electric shocks! Moreover, the human body is a good conductor. So it provides a resistance-free path for the current to flow from wire to body. Conductors have free electrons on its surface which allow current to pass through CHAPTER – 1 ELECTRIC CHARGES AND FIELD Did You know Electric charge, which can be positive or negative, occurs in discrete natural units and is neither created nor destroyed. EL E C TRI C C H ARG ES A N D FIEL D


Electric Field Assume there are point charges (sizes <<< r) P and Q placed r distance apart in a vacuum. Both charges create an electric field around them which ultimately is responsible for the force applied by the two on each other. The Electric Field around Q at position r is E(r) = kQ r 2 r̂ Where r is a unit vector of the distance r with respect to the origin. This value E(r) amounts to an electric field of each charge based on its position vector r. When another charge q is brought at a certain distance r to the charge Q, a force is exerted by Q equal to: FQ = kQq r 2 r̂ Now, there is an equal and opposite force exerted on Q by q which is equal to: Fq = kqQ r 2 r̂Hence, if q is a unit charge, the force applied is equal to field value. Electric Field due to a System of Charges If there is a system of charges q1, q2, ... qn in space with position vectors r1, r2, ... rn and the net effect of the Electric Charges are required to be calculated on a unit test charge q with position vector r placed inside the system, then it is attributed to a superimposition of Electric field values for all charges by Coulomb’s Law: E = E1 + E2 + ... + En = kq1/r1 2 + kq2/r2 2 + ... + kqn/rn 2 where En(rn) is the Electric Field value of charge n in the system with respect to position vector rn. Here, E is a vector quantity and its value are attributed to change in the position of source charges. Physical significance of electric field Electric Field under Static Condition: Static means 'at rest'. The charged bodies, under the static condition, experience an electric field surrounding them. The electric field is defined at every point and changes from point to point Electric Field under Electromagnetic Non-static Condition: This is the condition where the accelerated motion of the charge gives rise to electromagnetic waves and this propagates with a speed c passing on a force on another charge. Time-dependent magnetic and electric fields are connected with the transport of energy. Electric field lines The notion of the electrical field was first presented by the 19th-century physicist Michael Faraday. It was Faraday's understanding that the pattern of lines describing the electric field is an invisible reality. ss Since the electric field varies as the inverse of the square of the distance that points from the charge the vector gets shorter as you go away from the origin and they always point radially outwards. Connecting up these vectors to form a line Q. Two-point charges A and B, having charges +Q and −Q respectively, are placed at certain distance apart and force acting between them is F. If 25% charge of A is transferred to B, then force between the charges becomes (a) 4F 3 (b) F (c) 9F 16 (d) 16F 9 Sol. Ans. (c) 9F 16 In case I: F = − 1 4πε0 Q 2 r 2 ...(i) In Case II: QA = Q − Q 4 ,QB = −Q + Q 4 ∴ F ′ = 1 4πε0 (Q− Q 4 )(−Q+ Q 4 ) r 2 = 1 4πε0 ( 3 4 Q)( −3 4 Q) r 2 = − 1 4πε0 9 16 Q 2 r 2 ...(ii) From equations (i) and (ii), F ′ = 9 16 F