SUBTOPIC Charge units Electric field Electric force & Coulombs - PowerPoint PPT Presentation

SUBTOPIC • Charge units • Electric field • Electric force & Coulomb’s Law • Capacitance and unit • Capacitance and unit • Parallel plate capacitor • Dielectric constant and it’s function

Electric Charge Electric charge is a fundamental property of matter ; electric charges may be positive or negative . The atom consists of a small positive nucleus is surrounded by a negative electron cloud .

Electric Charge Is an intrinsic characteristic of the fundamental particles making up those objects; that is, it is a characteristic that automatically accompanies those particles wherever they exist. Charges with the same electrical sign repel each other ; and charges with opposite electrical signs attract each other.

Electric Charge - Lightning

Electric Charge SI unit of charge: the coulomb, C . All charges are integer multiples of the charge on the electron: n = 1, 2, 3,.. Conservation of charge : The net charge of an isolated system remains constant. Net charge of the universe is constant !!!

Electrostatic Charging Conductors � materials in which electric charges move freely Semiconductors are intermediate ; their conductivity can depend on impurities and can be manipulated by external voltages. Insulators � Insulators � � � � materials in which electric � � � materials in which electric charges do not move freely.

Electrostatic Charging An electroscope may be used to determine if an object is electrically charged.

Electrostatic Charging: FRICTION Charging by friction : This is the process by which you get “charged up” walking across the carpet in the winter. It is also the process that creates “static cling” in your laundry, and makes it cling” in your laundry, and makes it possible for you to rub a balloon on your hair and then stick the balloon to the wall.

Electrostatic Charging: CONDUCTION An electroscope can be given a net charge by conduction – when it is touched with a charged object, the excess charges flow freely onto the electroscope.

Electrostatic Charging: INDUCTION An electroscope may also be charged by induction , if there is a way of grounding it while charge is being induced.

Electrostatic Charging: POLARIZATION Charge may also be moved within an object – without changing its net charge – through a process called polarization. ( charge separation by polarization )

Electric Force For the two point of charges, depend directly to the product of the magnitude of the charges and inversely on the square root of the distance between them: Called Coulomb’s Law Called Coulomb’s Law q 1 q 2 r

Electric Force If there are multiple point charges , the force vectors must be added to get the net force.

��������� ��������� ��������� ��������� q 2 = +2nC q 1 = -1nC F 21 F 12 0.3m (a) Two point charges of -1.0nC and +2.0nC are separated by a distance of 0.3m, what is the electric force on each particle? y y q 1 = +2.5nC (0, +0.3m) r 31 q 3 = +3.0nC θ x θ (0, 0.4m) r 32 (0, -0.3m) q 2 = +2.5nC (b) What is the net electric force on q 3 ?

Solution: kq q (a) 1 2 F = F = 12 21 2 r 9 2 2 − 9 - 9 (9 × 10 Nm /C )( 1 × 10 C)(2 × 10 C) = 2 ( 0 . 3 m) - 6 = 0.2 × 10 N = 0.2 µ N y y q 1 = +2.5nC F 32 (b) F net = F 3 θ x θ F 31 q 2 = +2.5nC

Solution: (b) r 31 = r 32 = 0.5m 9 2 2 − 9 -9 kq q (9 × 10 Nm /C )( 2 . 5 × 10 C)(3.0 × 10 C) 2 3 F = = 32 2 2 r ( 0 . 5 m) = 0.27 µ N Taking into account the direction of F 31 and F 32 is symmetry – then y – components Taking into account the direction of F 31 and F 32 is symmetry – then y – components cancel. Thus, F 3 (the net force on q 3 ) acts along the positive x -axis and has magnitude of F = F + F = 2 F 3 31 32 31 � � 0 . 3 m � � − 1 o θ = tan = 37 � � 0.4m o F = 2 F = 2 F cos θ = 2 ( 0.27 µ N)cos37 = 0 . 43 µ N 3 31 32

��������� ��������� ��������� ��������� (a) What is the magnitude of the repulsive electrostatic force between two protons in a nucleus? Taking the distance from center to center of these protons to be 3 x 10 -15 m. a) If the protons were released from rest, how would the magnitude of their initial acceleration compare with that of the acceleration due to gravity on Earth’s surface, g ?

Solution: Given: r = 3 x 10 -15 m; q 1 =q 2 = +1.6 x 10 -19 C ; m p = 1.67 x 10 -27 kg (a) Using Coulomb’s Law; 9 2 2 -19 2 kq q (9 × 10 Nm /C )(1.6 × 10 C) 1 2 F = r = = 25 . 6 N e 2 - 15 2 (3 × 10 m) F 25.6N (b) 28 2 e a = = = 1 . 53 × 10 m/s - 27 1.67 × 10 kg m p 28 2 1.53 × 10 m/s a 27 = = 1 . 56 × 10 2 9 . 8 m/s g

Electric Field The electric field at any location is defined as follows: 2 F ( kqq / r ) kq on q + + SI Unit: N/C E = = = 2 q q q q r r + + + + The direction of the field E is the direction the force would be on a positive charge .

Electric Field Charges create electric fields, and these fields in turn exert electric forces on other charges. Electric field of a point charge :

��������� ��������� ��������� ��������� 1. Two point charges are placed on the x -axis as shown in Fig. below. Find all locations on the axis where the E = 0. q 1 = +1.5μC q 1 = +6μC x x 0.0 0.6

Solution kq kq 1 2 E = E or = 1 2 2 2 x ( d − x ) Where, d is the distance of q 2 , rearranging this expression, 1 ( q / q ) 2 1 = 2 2 x x ( ( d d − − x x ) ) With q 2 / q 1 = 4, taking square root of both sides: 1 q / q 1 2 � 2 1 = = 2 2 x ( d − x ) x d − x Thus; = d 0 . 6 m x = = 0 . 2 m 3 3

���������� ���������� ���������� ���������� y q 3 q 1 d d 30 o 30 o x 30 o d q 2 1. Fig. above shows three particles with charge q 1 = +2Q, q 2 = -2Q, and q 3 = -4Q, each a distance d from the origin. What net electric field E is produced at the origin? y - 8μC s s s x P + 2μC + 12μC 2. Find the electric field at point P due to the charges shown where s = 50cm.

Electric Field Electric field lines due to very large parallel plates: Q – magnitude of total charge on one of the plates ; A – area of one plate .

Electric Field Electric field lines due to like charges: (a) equal charges ; (b) unequal charges .

Electric Field

Conductors and Electric Fields Electric charges are free to move within a conductor; therefore, there cannot be a static field within the conductor: The electric field is zero inside a charged conductor. Excess charges on a conductor will repel each other, and will wind up being as far apart as possible. as far apart as possible. Any excess charge on an isolated conductor resides entirely on the surface of the conductor.

Conductors and Electric Fields There cannot be any component of the electric field parallel to the surface of a conductor; otherwise charges would move. The electric field at the surface of a charged conductor is perpendicular to the surface.

Conductors and Electric Fields The force from neighboring charges is less when the curvature of the surface is large: Excess charge tends to accumulate at sharp points, or locations of highest curvature, on charged conductors. As a result, the electric field is greatest at such locations.

PART 2 Electric Potential, Energy & Capacitance Electric Potential, Energy & Capacitance

Electric Potential Energy To move a charge from one point to another point in E , a work need to be • done Work done by external force to move a +ve charge (+q) from A to B in E • =F/q by a charge +Q state as: dr = charge displacement b b � � θ = angle between F’ and dr W = F ' dr = F ' cos θ dr F’ =F by E, but in different direction a a +Q +Q +q +q E=F/q E=F/q U A U B − ∆ U = U − U = W • When charge moves from UA to UB, energy changes A B • In general, electric potential energy given by � � U = F . dr = q E . dr kQq U = r

Electric Potential • Definition: Electric potential energy per unit charge U kQ � V = = E . dr = q r • Unit: Volt or JC -1 • For a number of Q1, Q2 and Q3 at distance r1,r2 and r3 from point P point P +Q1 r1 +Q3 r3 P r2 Q Q Q Q � 1 2 3 i V = k ( + + ) = k +Q2 r r r r 1 2 3 i

Electric Potential Energy & Electric Potential Difference Electric Potential Energy It takes work to move a charge against an electric field. Just as with gravity, this work increases the potential energy of the charge. Gravity !!!

Electric Potential Energy & Electric Potential Difference Just as with the electric field, it is convenient to define a quantity that is the electric potential energy per unit charge. This is called the electric potential . Electric potential difference SI unit of electric potential: Joule/Coulomb or the volt, V.