INTERACTION BETWEEN ELECTRIC CHARGES

Transcription

1 Publikacja współfinansowana ze środków Unii Europejskiej w ramach Europejskiego Funduszu Społecznego AUTHOR G. Jarosz INTERACTION BETWEEN ELECTRIC CHARGES When we rub plastic rods with a piece of fur, we find rods repel each others. The same effect is observed for glass rods rubbed with silk, but on the other hand the plastic rod rubbed with fur attracts the glass rot rubbed with silk. Two kind of electric charge names introduced by Benjamin Franklin ( ) positive negative Two positive charges or two negative charges repel each other. A positive charge and a negative charge attract each other.

2 Structure of Atoms ~10-10 m ~10-15 m proton: mass= kg, positive charge= C neutron: mass= kg, no charge electron: mass= kg, negative charge= C Helium Atom The charges of electron and proton are equal in magnitude. Materials can be divided into according to the ability of charge to move through them conductors They permit charge to move easily from one region of the material to another (e.g. metals). insulators Materials through which charge cannot move freely (e.g. rubber, glass, teflon, chemical pure water)

3 COULOMB S LAW r F21 F12 Charge of the same sign repel each other. q2 q1 r F21 F12 -q2 -q1 r 1 q1 q 2 F= 4π ε o r 2 -q1 F12 F21 q2 F12 - the force exerted by the charge 2 on the charge 1, F21 the force exerted by the charge 1 on the charge 2, q1 and q2 - magnitudes of charges, r - distance between the charges, εο permittivity constant equal to C2/(Nm 2) The electric force between two point charges is directly proportional to the product of the charges and inversely proportional to the square of distance between them (Charles Augustin Coulomb ( )).

4 ELECTRIC FIELD A charge particle sets up an electric field in the space around it. The electric field at point P is defined by: F E= qo N C F - force exerted on a test charge at point P, qo - a positive test charge. The test charge should be very small so the electric field at point P when qo is present has to be the same as when qo is absent. Electric Field Lines Electric field lines help us in visualization of electric field (the concept of field lines was introduced by Micheal Faraday ( )). An electric field line is drawn so that the electric field vector is tangent to it at an points. The electric field lines produced by a positive point charge point away from the charge. Electric field lines: show the direction of electric field, never intersect and their density corresponds to the magnitude of electric field.

5 Electric Field Lines Two equal and oposite charges (an electric dipole) Two equal positive charges

6 Electric Dipole in Uniform Elecric Field Two point charges with equal magnitude and opposite sign separated by a distance d make up an electric dipole. F=q E The net force on an electric dipole in a uniform electric field equals zero. The net torque with respect to the centre of the dipole is the sum of the torques: F_= - q E Fnet= 0 net =0.5 q E d sin 0.5 q E d sin net =q E d sin = p E sin ϕ the angle between p and E. or we can write down τ net τ net= p Ε where p a vector quantity known as an electric dipole moment. The magnitude of p is given by p=q d and it is directed from negative charge to positive charge. F_= - q E F=q E τ net= p Ε The net torque is directed into the page and tends to rotate the dipole.

7 Flux of an Electric Field Flux of electric field through a flat area is defined for uniform electric field by: A Φ E =E A scalar product Φ E=E A Φ E =E A cosϕ where A ϕ A - area vector. ϕ the angle between E and A. Φ E=E A cosϕ

8 The electric field through a closed surface can be found integreting the scalar product E da over this closed surface: The electric flux through closed surface is proportional to the number of electric field lines passing through that surface. ΦE= E da the loop indicates da vector of small that the integretion element of the area is to be taken over the closed surface Gauss' Law The electric flux through a closed surface is equal to the charge (qenc) that is enclosed by the surface, divided by εo: E da=qenc/εo For positive qenc the flux is outward, while for negative qenc inward. Publikacja współfinansowana ze środków Unii Europejskiej w ramach Europejskiego Funduszu Społecznego

9 Gauss' Law for an Infinite Plane Sheet of Charge Gauss' Law for a Point Charge E ds r q E S 2 ds E 1 E 1 2 S σ - charge per unit area A closed surface of radius r, centred on a point charge q. From symmetry we come to the conclusion that: E is perpendicular to ds at any point, E is directed outward from the centre, E is of the same magnitude, at all points in the distance r from the centre. Therefore, ΦE = 4 π r2 E which leads to: From symmetry we come to the conclusion that: E is perpendicular to the plane sheet, E is directed outward from the sheet, E is of the same magnitude, at all points in the distance x from the sheet. ΦE=Φ1Φ2 Φ1=0, since E is perpendicular to ds, qenc = q Φ2=2E S, E = q/(4 π r2 εo) qnet=σ S. and Therefore, since E is parallel to S, E= σ/(2 εo)