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Transcript
Pavitra Gupta 9312281591 Pavitra Gupta 9312281591 ELECTRIC CHARGES and COULOMB’S LAW Q.1 Two charged particles placed at a distance of 1cm. What can be the minimum force between them? [2.3 x 10-24N] Q.2 Two positive point charges 0.1m apart repel each other by a force of 18 N. If the sum of two charges is 9 C, find the charges. Q.3 [5C, 4C] Two free point charges +4q and +q are at a distance of ‘a’. Where should a third point charge Q be placed between them so that the entire system is in equilibrium? What will be the magnitude and sign of Q? Q.4 [Q= - 4q/9 at 2a/3 from +4q] Two particles, each having a mass of 5g and charge 10-7 C, stay in limiting equilibrium on a horizontal table with a separation of 10cm between them. The coefficient of friction between each particle and the table is same. Find the value of this coefficient. Q.5 [=0.18] Two similarly and equally charged identical metal spheres A and B repel each other with a force of 2 x 10-5 N. A third identical, uncharged sphere C is touched with A and then placed at the mid point between A and B. What is the net electric force on C? Q.6 [2 x 10-5 N towards A] Charges q1 = +1.5 mC, q2 = +0.2 mC and q3 = – 0.5mC are placed at points A, B and C respectively of a triangle right angled at B. If AC = 1.2m and BC = 0.6m, calculate magnitude of resultant force on q2. [3125 N] Q.7 Two opposite corners of a square carry Q charge each and the other two opposite corners of the same square carry q charge each. If the resultant force on q is 0, how are Q and q related? Q.8 [q = - 2 2 Q] A pith ball A of mass 9 x 10-5 kg carries a charge of 5 C. What must be the magnitude and sign of the charge on another ball B held 2 cm above ball A, such that A remains suspended stationary above the [7.84x10-12C] ground? Q.9 Two point charges of 6.5 x 10-7 C each are separated by a distance of 50 cm. What is the force of repulsion between them if (i) they are placed in air? (ii) they are placed in water? [1.521 N, 0.019 N] Q.10 Four point charges 2C, –5 C, 2 C and –5 C are placed at the corners A, B, C and D respectively, of a square ABCD of side 10 cm. Find the force on a charge of 1 C placed at the centre O of the square. Q.11 A polythene piece rubbed with wool is found to have a negative charge of 3 x 10-7 C. (i) Find the number of electron transferred and state whether electrons are transferred from wool to polythene or [2x1012 from wool to polythene, yes] otherwise. (ii) Is there a transfer of mass? Q.12 Calculate the force between 2 alpha particles separated by a distance of 1.6 x 10-15 m. [360 N repulsive] Q.13 Three equal charges, 2.0 x 10-6 C each, are held fixed at the three corners of an equilateral triangle of side 5 cm. find the coulomb force experienced by one of the charges due to the rest two. [14.4 N at 30 with a side of ] Pavitra Gupta 9312281591 -1- Pavitra Gupta 9312281591 Pavitra Gupta 9312281591 Pavitra Gupta 9312281591 ELECTRIC FIELD Q.1 Q.2 A test charge 2nC, placed at origin, experiences a force of 8 x 10-4 N in the positive y – direction. Find electric field at origin. What would be the force on charge – 4nC placed at origin? [4x105 N/C, -16x10-4 N] Find the magnitude of electric field which can balance a deuteron of mass 3.2 x 10-27 kg. [19.6x10-8N/C] Q.3 A charged particle of mass 1.0 g is suspended through a silk thread of length 40 cm in a horizontal electric field of 4.0 x 104 N/C. If the particle stays at a distance of 24 cm from the vertical line passing through its point of suspension, find the charge on the particle. [1.8 x 10-7 C] Q.4 ABC is an equilateral triangle of side 5 cm. Two charges 50/3 x 10-3 C are placed at A & B respectively. Calculate magnitude and direction of field at C. [6 x 104 N/C, ║ to AB] Q.5 Two charges 10 C are held at 5 mm apart. Calculate their dipole moment. What is the electric field intensity at a distance of 15 cm from the centre of dipole on its axial line? [5 x 10-8 Cm, 2.7 x 105 N/C] An electric dipole of length 2 cm is placed with its axis making an angle of 30 with a uniform electric field of 105 N/C. If it experiences a torque of 10 3 Nm, calculate (i) magnitude of charges on dipole (ii) potential energy of dipole. [1.732 x 10-2C, - 4.64 J] Q.6 Q.7 In a certain region of space, electric field is along the positive z – direction whose magnitude increases uniformly at the rate of 105 N/Cm along the positive z – direction. What are the forces and torque experienced by dipole of dipole moment 10-7 Cm in the negative z – direction? [-10-2 N, 0] Q.8 An oil drop of 12 excess electron is held stationary under a constant electric field 2.55 x 104 V/m in Milikan’s oil drop experiment. The density of oil is 1.26 g/cm3. Find the radius of the drop. (Take g = 9.81 m/s2) [9.81 x 10-4mm] Q.9 A copper ball of density 8.6 g/cm3, 1 cm in diameter is immersed in oil of density 0.8 g/cm3. If the ball remains suspended in oil in an electric field of 36000 N/C acting in upward direction, what is the charge on the ball? Q.10 Calculate the electric field intensity at point P ( 0, 3, -1 ) due to a charge of – 2 C placed at point 3 A ( -3, 0, -4 ). [ 2 3 10 ( ˆi ˆj k̂) N/C] 9 Q.11 A charge 4 x 10-9 C is distributed uniformly on a ring of radius 0.3 m. Find field intensity at a point on the axis of ring at 0.4 m from centre and also at the centre. [115.2N/C, 0] Q.12 Two point charges of +3 x 10-19 C and + 12 x 10-19 C are separated by a distance of 2.5 m. Find the point on the line joining them at which the electric field intensity is zero. [5/6 m from 3 x 10-19 C] Q.13 Two point charges 3C and – 3 C are located 20 cm apart in vacuum at point A and B respectively. (i) What is the electric field at the mid point O of the line AB. (ii) If a negative charge of magnitude 1.5 x 10-9 C is placed at this point, what is the force experienced by this charge? [5.4x106 N/C along OB,8.1x10-3N along OA] Two charges 10C are placed 5 mm apart. Find the electric field at (i) point P on the axis of the dipole 15 cm away from its center O on the side of positive charge, (ii) point Q, 15 cm away from O on a line passing through O and normal to axis of the dipole. [2.7x105N/C along BP,1.33x105N/C along BA] Q.14 Pavitra Gupta 9312281591 -2- Pavitra Gupta 9312281591 Pavitra Gupta 9312281591 Pavitra Gupta 9312281591 ELECTRIC POTENTIAL and ELECTRIC FLUX Q.1 The electric field and potential at a point due to a point charge are 30 N/C and 15 J/C respectively. Find the distance of point from the charge and the magnitude of the charge. [0.5 m, 0.833 x 10-3 C] Q.2 If 100 J of work is done to move a charge of 4 C from a place of potential – 10 volt to another place where potential is V volt, find the value of V. [15 V] Q.3 An electric field of 20 N/C exists along x – axis. Calculate potential difference VB – VA where coordinates of pints A and B are ( 4m, 2m ) and ( 0, 0 ) respectively. [80 V] Q.4 A point charge 10-8 C is situated at origin. Find the potential difference between points A( 4, 4, 2 ) and B(1, 2, 2 ). [-15 V] Q.5 Two positive point charges 10 C and 5 C are 1 m apart. Find the work done in bringing them 0.5 m apart. [0.45 J] Q.6 Two electrons, each with a velocity of 106 m/s are released towards each other. What will be the closest distance of approach between them? [2.56 x 10-10 m] Q.7 Two identical particles, each of mass 10 g and carrying charge 2 x 10-4 C, are kept at a distance of 10 cm and released. What would be the speed of particles, when separation becomes infinitely large? [600 m/s] An infinite thin plane sheet of charge density 10-8 C/m2 is held in air. How far apart are two equipotential surfaces, whose potential difference is 5 V? [8.85 x 10-3 m] Q.8 Q.9 (a) A rectangular frame of wire 25 cm x 15 cm is placed in uniform electric field of 2 x 104 N/C such that the plane of frame is normal to the field. Find electric flux linked with the frame. (b) Find electric flux if this frame is converted into a square. [750 Vm; 800Vm] Q.10 (a) A box encloses an electric dipole of charges 5C and length 10 cm. What is the total electric flux through the box? (b) If the number of electric field lines from a closed surface are 1000, calculate the charge enclosed by the surface. [0; 8.85 x 10-9 C] Q.11 The electric field is ( 5 î 4 ˆj 4 k̂ ) 10 N/C in a region. Calculate electric flux due to this field over an area of ( 2 î ˆj ) 10 -2 m2. [6000 Nm2/C] 5 If the potential in the region of space around point ( –1m, 2m, 3m ) is V = (10 x2 + 5 y2 – 3 z2 ) volts, calculate the three components of electric field at this point. [Ex = 20V/m; Ey = -20 V/m; Ez=18 V/m] Q.13 An electric dipole consists of charges of 2 x 10-8 C separated by a distance of 2 mm. It is placed near a long line charge of density 4 x 10-4 C/m as shown in the figure, such that negative charge is 2 cm from the line charge. -q +q Find the force acting on the dipole. Line charge Q.12 2 cm [0.66 N] Pavitra Gupta 9312281591 -3- Pavitra Gupta 9312281591 Pavitra Gupta 9312281591 Pavitra Gupta 9312281591 CAPACITANCE Q.1 A spherical conductor has a surface charge density of 0.07 C/m2. When charge is increased by 4.4 C the density changes by 0.084 C/m2. Find the radius & initial charge. [2.04 m; 11/3 C] Q.2 If 64 small mercury drops each charged to 220 V coalesce, what is the potential of the bigger drop? [3520V] Q.3 At what distance should the plates of area 0.2 m x 0.1 m of air capacitor be placed in order to have a capacitance as a spherical conductor of radius 0.5 m? [3.18 mm] Q.4 A parallel plat air capacitor having plate area 6 x 10-3 m2 and plate separation 3 mm is connected to 100 V supply. Calculate charge on each plate. Explain what would happen when a 3 mm thick mica sheet ( = 6 ) is inserted between plates (a) while voltage supply remains connected (b) after supply is connected? [1.77 x 10-9 C; 1.06 x 10-9 C; V=16.7 V] Q.5 Calculate the value of C for the given figure, if equivalent capacitance between P and Q is 30 F. [60F] 20F 20F P Q C 20F Q.6 What is the capacitance of arrangement of 4 plates each of area A at a distance d in air for the given figure? d d A (i) A B (ii) d d [20A/d] B d [30A/d] Q.7 A parallel plate capacitor is filled with two dielectrics as shown in the figures. Calculate the capacity of each. (i) (ii) [ Q.8 0A ( 1 2 ) ] 2d Calculate the equivalent capacitance between A and B for the following figure: [ 2 0 A 1 2 ] d ( 1 2 ) A B 5F 10F 15F 30F [15F] 4 F Q.9 Q.10 Q.11 Q.12 Take potential of B to be zero in the given figure. (a) Find potential at C & D. (b) If a capacitor is placed between C and D, what charge will appear on this capacitor? [50/3 V;50/3 V; 0] C 8 F A B 3 F D 6 F 50 V A 4 F capacitor is charged by 200 V supply. It is disconnected from supply and connected to another uncharged 2 F capacitor. How much electric energy is lost by first capacitor? [2.67 x 10-2 J] A capacitor of 20 F and charged to 500 V is connected in parallel with another 10 F capacitor charged to 200 V. Find the common potential. [400 V] Two capacitors of capacitances C1 = 3 F and C2 = 6 F arranged in series are connected in parallel with 3rd capacitor C3 = 4 F. The arrangement is then connected to 6 V battery. Find total energy stored in the arrangement. [1.08 x 10-4 J] Pavitra Gupta 9312281591 -4- Pavitra Gupta 9312281591 Pavitra Gupta 9312281591 Q.13 Pavitra Gupta 9312281591 In Van de graf generator, spherical shell of metal has 15 x 105 V potential. The dielectric strength of surrounding gas is 5 x 107 V/m. Find the minimum radius of the shell. [0.3 m] Pavitra Gupta 9312281591 -5- Pavitra Gupta 9312281591