Electric Field and Potential Questions and Answers

A hollow spherical conducting shell of inner radi r and outer radius r has a charge Q A charge qis placed at the centre of the sphere The surface charge densities on the inner and outer surfaces of the sphere will be respectively q q 1 4 and 471 2 2 101 q Q 9 2 4 q 4 r 2 and Q q 4 r 2 Q 9

P123 The distance between the plates of a plane capacitor is d and the area of each plate is A As shown in the figure both plates of the capacitor are earthed and a small body carrying charge Q is placed between them at a distance x from one plate A Q What charge will accumulate on each plate

figure below shows the path of a positively charged particle 1 through a rectangular region of uniform electric field as shown in the figure What are the direction movement of particles 2 3 and 4 20 10 por Top at sana sana ang nang od tour Down 3 04

Two small spheres each of mass m and charge q are tied from the same rigid support with the help of silk threads of length L They make angle with the vertical as shown in the figure If length L is decreased then angle 0 with the vertical L L m

Find whether the given electric fields are possible or impossible electric field E xyi 2yzj 3xzk and E y i 2xy z2 j 2yzk a Only E is a possible electrostatic field b Both E and E are possible electrostatic field c Only E is a possible electrostatic field d Both E and E are impossible electrostatic field

X and Y are large parallel conducting plates close to each other Each face has an area A X is given a charge Q Y is without any charge Point A B and C are as shown in the figure Find the incorrect option A 1 the field at B is 2 the field at B is X Q 250A ZA B C 3 the fields at A B and C are of the same magnitude 4 the fields at A and C are of the same magnitude but in opposite directions

charge 0 4 C due to another small sphere of charge 0 8 C in air is 0 2 N a What is the distance between the two spheres b What is the force on the second sphere due to the first

16 Electric Potential is zero at point q B A D E C 41 3 ir e d dt 4 400 s 16 far 37 1 A D only 2 B C D only 3 A B C D E 4 None of these 17 The current in solenoid of 240 turns having a length 12 cm 17 240 and a E MON 9 1 hac A 2 3 A B 4

As a result of change in the magnetic flux linked to the closed loop shown in figure an emf V volt is induced in the loop The work done in joule in taking a charge q coulomb once along the loop is a qV c 2qV b zero qV d 2

question contains statements given in two columns which have to be matched Statements A B C column I have to be matched with statements p q r s t in column II A spherical cavity of radius r is made in a conducting sphere of radius 2r A charge q is kept at the cetnre of cavity as shown in the figure Match the following Column Total field at 4r 0 0 Field at 4r 0 0 due to a Total field at 1 2 0 0 Field at 1 2 0 0 due to g p Kq 16r q 4Kg r r Kq 25 5 4Kq 9r 0 0 2 Column it

25 Four point charges 9A 9B 2 C q 5 C qc 2 C and qD 5 C are located at the corners of a square ABCD of side 10 cm What is the force on a charge of 1 C placed at the centre of the square

Figure shows some equipotential lines distributed in space A charged object is moved from point A to point B 20V 40V 30V 40V 30V HURL 48 1 46 1 B A B A B 10V 30V 50V 10V 20V 50V 10V 20V 40V 50V Figure I Figure II Figure III A The work done in figure i is the greatest M PAPER B The work done in figure ii is least C The work done is the same in figures i ii iii D The work done in figure iii is greater than figure ii but equal to that in figure i

25 In a certain region of space electric field is along the z direction throughout The magnitude of electric field is however not constant but increases uniformly along the positive z direction at the rate of 105 NC 1 per metre What are the force and torque experienced by a system having a total dipole moment equal to 10 7 cm in the negative z direction

26 A hollow charged conductor has a tiny hole cut into its surface Show that the electric field in the hole is o 2con where n is the unit vector in the outward normal direction and o is the surface charge density near the hole

Four point charges are placed at the corners of a square of side a as shown in the figure A charge q is slowly displaced from P to P2 then work done in displacing the charge Q P a Q Positive O Negative Zero P English Insufficient information

27 Obtain the formula for the electric field due to a long thin wire of uniform linear charge density E without using Gauss s law Hint Use Coulomb s law directly and evaluate the necessary integral

97 At a distance from a uniformly charged long wire a charged particle is thrown radially outward with a velocity u in the direction perpendicular to the wire When the particle reaches a distance 2 from the wire its speed is found to be 2 u The magnitude of the velocity when it is a distance 4 away from the wire is ignore gravity a 3 u c 2 2 u b 2u d 4u

electric field pointing from the corner A towards the corner C What the charges induced on each rod 5 Three identical point charges are placed on the vertices of an equilate triangle At how many places within the triangle electric field vanish

1 Which electric field is responsible for the proton s trajectory as shown below 1 2 4 F F Parabolic trajectory f is in dirt of field EADER TEST SERIES JOINT PACKAGE RANK BOOSTER COURSE

91 4 1 93 1 A frictionless non conducting inextensible thread of length wears three beads of positive charges 91 92 and 93 The ends of the thread are connected to make a knotless loop Length of the thread is so large as compared to the size of the beads that the beads can be treated as point particles The system is in a state of equilibrium with beads at vertices of a triangle a Find lengths 1 12 and 13 of the sides of the triangle b What relation the charges 91 92 and q3 must bear to establish the above mentioned state of equilibrium

AB is 1 meter long uniform wire of 10 ohm resistance The other data are as shown in the circuit diagram Calculate a potential gradient along AB and length AO of the wire when the galvanometer shows b no deflection A E 2V 1 20 0 30 150 E 1 5V

Two substances are identical except that the electron mean free time for substance A is twice the electron mean free time for substance B If the same electric field exists in both substances the electron drift speed in A is A the same as in B 3 twice that in B C half that in B O four times that in B E one fourth that in B

Q22 Two resistors have different temperature coefficient of resistance a 1 and a 2 What will be the equivalent temperature coefficient of their pa combination A a 1 a2 B a1 2 2 C a 1 a 1 D a 1 a 2

elect the correct statement If electric field is zero at a certain point then potential should be zero at that point If electric field is not zero at a certain point then potential should not be zero at that point If potential is zero at a certain point then electric field should be zero at that point If potential is zero at a certain point then electric field at that point may or may not be zero

9 Keeping the voltage of the charging source constant what would be the percentage change in the energy stored in a parallel plate capacitor if the separation between its plates is decreased by 10 CBSE 09 11 1 increase

Two spheres of radii 1 cm and 2 cm have been charged with 1 5 x 10 8 and 0 3 x 10 7 coulombs of posiitve charge When they are connected with a wire charge 1 will flow from the first to the second 2 will flow from the second to the first 3 will not flow at all 4 may flow either from first to second or from the second to first depending upon the length of the connecting wire

In the rectangle shown below the two corners have charges q 5 0 C and q 2 0 C 91 SHE 9 A B 15 cm 5 cm 922 2ML

2 Two spheres of radii R and R having equal charges are joined together with a copper wire If V is the potential of each sphere after they are separated from each other then the initial charge on both spheres was 1 R R V 3 R R 3k 2 Z R R 2k V R R 4 K R R k

13 In a uniform electric field the potential of origin is V and at each of the points a 0 0 0 b 0 2 0 0 c The potential at a b c will be 1 3 V 2 V 2 3V 2 4 V I

Two fixed solid spheres of charges Q and KQ are separated by a distance 6R A charge q is to be projectes along the line joining their centres so that it can reach the surface of other solid sphere of charge KQ Bondh RA q m min i If k 4 find minimum velocity to be given 6R 2R kQ

A conducting sphere of radius R carries a charge 30 as shown in Figure It is surrounded by linear dielectric material of relative permittivity e out of radius a a Find the electric field at all points b Find the electric potential at the center of the sphere taking the potential at infinity as zero 3Q R

Two particles A and B having equal charges are placed at distance d apart A third charged particle placed on the perpendicular bisector of AB at distance x The third particle experiences the maximum force when O X X O X X d 2 2 d 2 2 d 3 2

Paragraph 2 A very long thick plate has a uniform positive volume charge density given by p x po for 2 is a positive constant d is the thickness of the plate and x 0 is the centre of the plate 34 d a 2 1 pAa 3 p Aa 2 Use Gauss law to find E a d 2 1 Pale 3 Pa 2 d 2 0 x axis 32 What is the symmetry of the electric field for this object 1 Planar 3 Cylindrical 2 Spherical 4 None of these 33 How much charge is contained in a Gaussian pillbox of cross sectional area A and thickness 2a where 2 2p Aa 4 4p Aa d 2 2p al 4 4p ale x 2 where d 35 How much charge is contained in a Gaussian pillbox of surface area A and thickness 2a where a 2 1 p Ad 2 2p Ad

A wire AMB is placed along y axis having linear charge density C m The electric field intensity at point P is PM 0 1 m B 33 1 08 x 10 1 A V m 1 08 x 1010 A V m 1 54 x 10 1 A V m 1019 V m

If the electric field just outside a thin conducting sheet is equal to 3 N C determine the surface charge density on the conductor Select one a 8 85 pC m2 b 35 4 pC m2 c 17 7 pC m2 d 53 pC m2 e 26 5pC m2

Paragraph for Questions 6 and 7 The electric potential varies in space according to the relation V 3x 4y 5 volts where x and y are in meters A particle of mass 10 g starts from point 2m 3 2 m 0 under the influence of this field The charge on the particle is 10 C Neglect gravity The component of electric field in X direction is A 3Vm B 4 Vm C 5 Vm The magnitude of acceleration of particle is A 1 x 10 m s B 3 x 10 m s C 5 x 10 m s D 7 Vm D 7 x 10 m s

Under the influence of the Coulomb field of charge Q a charge q is moving around it in an elliptical orbit Find out the correct statement s 1 The angular momentum of the charge q is constant 2 The linear momentum of the charge q is constant 3 The angular velocity of the charge q is constant 4 The linear speed of the charge q is constant

Electric dipole is placed at origin as shown Point A B C D are at distance r from origin then match the List I with List II List I P Electric potential at A Q Electric potential at B R Electric potential at C S Electric potential at D Code P A 3 B 4 C 1 2 1 2 3 List II KP sin 0 r kP cos 0 KP sin 0 r KP cos 0 r X ASSROOM

Two identical small bodies each of mass m and charge q are suspended from two strings each of length from a fixed point This whole system is taken into an orbiting artificial satellite then find the tension in strings Kq 1 2mg 1 Kq 4 2 3 2mg Kq 1 2 Kq

C 200 V m 100 V m D 200 V m 100 V m Figure shows a charge configuration with its equipotential surfaces and electric field lines placed in x y plane Mark INCORRECT statement DIGIT E B D A Potential gradient is positive along CD B Potential gradient is negative along EF C If a positive charge particle is constrained to move along line AB it will have constant potential energy D A positive charge particle released from rest at C will begin to move in direction DC

The axis of a long hollow metallic cylinder inner radius 1 0 cm outer radius 2 0 cm coincides with a long wire The wire has a linear charge density of 4 0 pC m and the cylinder has a net charge per unit length of 5 0 pC m Determine the magnitude of the electric field 3 0 cm from the axis Select one a 10 N C O b 7 2 N C C 5 N C d 5 4 N C e 9 N C

A charge of 2 C is uniformly distributed on a spherical shel of radius 5 m Electric potential at the centre of sphere is Zero 4 5 10 V 7 2 x 10 V 3 6 10 V

7 Find the dipole moment of given configuration if P QR where R is the radius of the circle 8 30 A 3P C 3 2P An electric dipole kept in an uniform electric field may experience GITAL C D 4P

In the figure below a neutral insulating disk of mass M and radius R is pivoted at the center A small charge q having negligible mass is fixed to one edge and a charge of q having negligible mass is fixed to the opposite edge so that the line between the two charges makes a small angle with an applied uniform electric field E as shown A The torque on the disk is 2qRE sine B The angular frequency with which the disk oscillates C The angular frequency with which the disk oscillates D The torque on the disk is RE sine 4Eq MR 2Eq MR 9 M

Two point charges 4 C and 4 C are placed at a distance 1 5 m Total number of points except infinity where potentia due to system of charges is zero One Three Two

The electric field intensity at a point at distance 4 m from a charge is 4 V m The amount of work in bringing a charge of 4 coulomb from infinity to same point is 8 J 16 J 64 J 32 J

n the figure shown a point charge 2Q is placed at the centre The two concentric thin conducting spherical shells of radi R and 2R shown have charges Q and 2Q respectively Find the amount of heat generated in J after the shell of adius R is earthed Take R 1 cm Q 1 C 0 20 2R

A thin quarter ring of radius 2R has a positive charge distributed uniformly over it The net field E at centre O is 4 O O O 20 i FER 16 CR Q STER 4x soR 20 TER 16n R Q STER

Charges q Q and q are placed at equal distance on a straight line If the total potential energy of the system of three charges is zero then find the ratio Q q q Q O 1 2 O 1 4 O 2 3 3 4 2r 9

ng spheres A and B are kept very near to each other A is positively charged and B is earthed then true statement is 4 A O B 1 A C Y A Charge on B zero B Potential at B is zero C Charge is uniformly distributed on A D Charge is non uniformly distributed or sphere A funda 19 2 A D