Electric Field and Potential Questions and Answers

Figure I igure II P P 18 Consider a cube as shown in the figure I with uniformly distributed charge in its entire volume Intensity of electrical field and potential at one of its vertex P are Eo and Vo respectively A portion of half the size half edge length of the original cube is cut and removed as shown in the figure II Find modulus of electric field and potential at the point P in the new structure a c Eo 2 3E 4 and and 3V 4 7Vo 8 3E b and 4 7E 8 d and Vo 2 7V 8

17 A cube made of an insulating material has uniform charge distribution throughout its volume Assuming electric potential due to this charged cube at infinitely distant places to be zero potential at the centre is found to be Vo What is electric potential at one of its corners a Vo c Vo 4 b Vo 2 d VJ8

The flux entering and leaving a closed surface are 5 x 105 and 4 x 105 SI unit respectively then the net charge inside the surface will be 8 85 x 10 7 C 8 85 x 10 7 C 8 85 10 6 C min sec 7 965 10 6 C

27 Two particles each of mass 100 g and charge 10 C are released on a horizontal plane at a distance 1 0 m from each other Coefficient of friction between the particles and the plane is 0 1 and acceleration of free fall is 10 m s Maximum speed acquired by the particles after they are released is closest to a 2 0 m s c 3 0 m s b 2 8 m s d 4 2 m s

An electric dipole of dipole moment p 6 x 10 4 C m is placed in a uniform external electric field of intensity 2x 105 105 N figure The angle between net electric field with external electric field E at point A will be r r 3m O 45 0 37 53 60 A E E as shown in the

In the given figure the capacitors C C C C have a capacitance 4uF each If the capacitor C has a capacitance 10 F then effective capacitance between A and B will be ATIMS 2002 A C C C 0 C 3 6uF B 4 8 F

Two small spheres of masses m and my with charges Q and Q are suspended with insulating threads of lengths L and L such that centres of spheres are in level www If 8 82 then which of the following condition is necessary O m m O m m but Q Q O Q Q OL L2 Q L m 0 m Q

Given a square frame of diagonal length 2r made of insulating wires There is a short dipole having dipole moment P fixed in the plane of the figure lying at the center of the square making an angle as shown i figure Four identical particles having charges of magnitude q each and alternatively positive and negative sign are placed at the four corners of the square Select the correct alternative s q Electrostatic force on the system of four charges due to dipole is 6kPq r3 Electrostatics force on the system of four charges due to dipole is 6kPq r3 cos A q Net torque on the system of four charges about the centre of the square due to dipole is zero r 3kPq r Net torque on the system of four charges about the centre of the square due to dipole is r Save

The figure shows two identical metallic plates kept parallel to each other and charged as shown Calculate the surface charge density in C cm2 that will appear on the side of plate I which is facing plate II Given Q 200 0 C and plate surface area 100cm 3Q Q

Neganve Marks The figure shows two identical metallic plates kept parallel to each other and charged as shown Calculate the surface charge density in C cm that will appear on the side of plate I which is facing plate II Given Q 200 0 C and plate surface area 100cm Q 8 in other cases 4 5 3Q Plate I Plate II

There are n infinite metal plates arranged parallel to each other as shown Q Q Q3 charges on these plates Charge Q on the left surface of leftmost plate in the arrangement is I 1 0 To O O Q Q Q3 n Q Q Q3 Qn 2 Zero Indeterminate as distances between different plates are not given Qn are respective

are arra 32 The conducting shells A and B are shown below If charge on the shell B is q then electric flux linked with the spherical gaussian surface S is 1 619 Q 2 200 G

Four charge of 1 C 1 C 1 C and 1 C are placed at the vertices of a square of side 2 cm in sequence Net force experienced by 0 1 C charge at the centre of square 1 9 N 2 18 N 3 36 N 4 Zero

6 A cube of side a has a charge q at each of its vertices The net electric field intensity at its centre is r is the distance between a corner and the centre and k 1 Zero 1 ARE 12qX 3 k 12q 2 2 K 2 20 4 k6q

Four charges of1 c 2 C 3 C and 6 C are placed one at each corner of the square of side 1m The square lies in the x y plane with its centre at the origin O The electric potential is non zero at Origin O The electric potential is zero everywhere along the x axis only if the sides of the sqaure areparallel to x and y axis The electric potential is zero everywhere along the z axis for any orientation of the square in the x y plane The electric potential is not zero along the z axis except at the origin

1 15 You are travelling in a car during a thunder storm in order to protect yourself from lightening would you prefer to 1 Remain in the car 2 Take shelter under a tree 3 Get out and be flat on the ground 4 Touch the nearest electrical pole

3 If E 0 V cannot be zero The electric field in a region is directed outward and is proportional to the distance r from the origin Taking the electric potential at the origin to be zero the electric potential at a distance r 1 is uniform in the region 2 is proportional to r Sis proportional to r 4 increases as one goes away from the origin

3 3 3 A sphere of radius 1 cm has potential of 8000 V The energy density near the surface of sphere will be 2 8 x 10 J m 3 32 J m 42 83 J m 1 64 105 J m X 2 drons assumed spherical each charged to a potential energy U coalesce to a single drop the

A positively charged ball hangs from a silk thread We put a positive test charge qo at a point and measure F qo then it can be predicted that the electric field strength E 1 F qo 2 F go 3 F qo 4 Cannot be estimated

In the figure given the potential difference between A and B in steady state will be 1uF 3 F HH 3 F V 2002 ww B 1 F 1 F 100V 2 25 V 1 20 V 3 75 V In the above question the potential difference between B and C in steady state will be 4 100 V 2 25 V 4 75 V 1002 3 50 V joined with capacitors of

29 If a uniformly charged spherical shell of radius 10 cm has a potential V at a point distant 5 cm from its centre the the potential at a point distant 15 cm from the centre will be 1 V 3 2 2V 3 3 2 V 3 Particle 4 3V

Which graph best represents the variation of electric potential as a function of distance from the centre of a uniformly charged solid sphere of charge of radius R V4 V4 1 3 R 2 4 V R r R r

Four point charges of charge 1 C each are placed at four corners of a square of side 2 m The work done in removing a charge 2 C fr centre of square to infinity is 1 28 J O 19 61 J O 50 9 mJ 4 83 J View in English

A hollow conduct sphere is placed in an electric field produced by a point charg figure Let V and V be the electrostatic potential at points A and B respectively Then 1 VA VB 2 VB VA 3 VB VA 4 Relation cannot be determined with the given information ACITORS AND CAPACITANCE B A P onstant verywhere

Problem 9 Two straight nonconducting wires parallel to the z axis pass through points O and A as shown in figure below The wires carry equal and uniform charge density 0 4 C m Determine the electric field at point P EA 45 P Eo 8 0 m

Two point charges of 1 0 C are kept stationary 2 m apart How much work is needed to be done to bring them 1 m apart 2 1 4 5 mJ 3 45 mJ An particle is accelerated from root thro 10 6 10 2 9 mJ 4 90 mJ tontial of Y volts Its final kinetic energy is

Electric Potential due to a Point Charge Electric Dipole System of Charges and Charged Bodies 4 Three isolated equal charges are placed at the three corners of an equilateral triangle as shown in figure The statement which is true for net electric potential V and net electric field intensity E at the centre of the triangle is q 94 1 E 0 V 0 3 V 0 E 0 O q 2 V 0 E 0 4 V F 0

An electric dipole of length 2 cm is placed with its axis making an angle of 30 to a uniform electric field 105 N C If it experiences a torque of 10 3 N m then potential energy of the dipole 1 10 J 3 30 J 2 20 J 4 40 J

12 Two concentric hollow conducting spheres of radius r and R are shown The charge on outer shell is Q What charge should be given to inner sphere so that the potential at any point P outside the outer sphere is zero 1 Qr R 3 Q R X 2 4 P QR r 2QR

Four charges of same magnitude q are placed at four corners of a square of side a The value of electric potential at the centre of the square will be Where k 1 1 4 0 4kq 4kq 3 2a 2 4 2 kq a 4 kq a 2

A charge of 10uC is placed at the origin x y coordinate system The potential differenc between two points 0 a and a 0 in volt will b 1 all 3 9 104 a 9x104 2 9 104 a 2 4 Zero

The potential at a point 0 1 m from an isolated point charge is 100 volt The nature of the point charge is 1 Positive 2 Negative 3 Zero 1 Either positive or zero

A conducting shell of radius R has charge Q Electrostatic force between two parts of the shell which are on either sides of a plane that is at a distance r r R from the centre of the shell is Q Q b 32 R a c 1 7 R Q p 1 32 R R d 2 32 R 327 Q 32 E R 1 5 R 1 1 R

0 Two spheres of radii R and R respectively are charged and joined by a wire The ratio of electric field of spheres is R 2 1 R2 R 3 R R 2 R 2 4 R R

9 Two insulated charged conducting spheres of radii 20 cm and 15 cm respectively and having equal charge of 10 C are connected by a copper wire and then they are separated Hence 1 Both spheres will have equal charges 2 Surface charge density on the 20 cm sphere will be greater than that on the 15 cm sphere 3 Surface charge density on the 15 cm sphere will be greater than that on the 20 cm sphere 4 Surface charge density on the two spheres will be equal

22 In an arrangement of two concentric conducting shells with centre at origin and radii a and b a b charges Q and Q are given to inner and outer shell then the potential V at a distance r from the Z origin is r a 1 V 5 3 V kQ kQ a b kQ kQ a r kQ KQ r a Q Q r 2 V 2 4 V k No Ja If the charge

2 0 cm An 20 Two charges q 3 0 C and q2 4 0 C initially are separated by a distance r external agent moves the charges until they are r 5 0 cm apart 1 How much work is done by the electric field in moving the charges from r to r Is the work positive or negative ii How much work is done by the external agent in moving the charges from r to r Is the work positive or negative

Consider a hollow spherical conductor that has a potential of 300 volts at its outside surface The potential inside the hollow space must be a Zero at the center and rising to something less than 300 V at the edge of the hollow space b Zero at the outer part and rising to 300 volts at the center c It depends on the ratio of outer and inner radii d Zero everywhere e 300 V everywhere 150 V everywhere

Q23 Figure shows a ball having a charge q fixed at a point A Two identical balls having charges q and q and mass m each are attached to the ends of a light rod of length 2a The rod is free to rotate about a fixed axis perpendicular to the plane of the paper and passing through the mid point of the rod The system is released from the situation shown in figure Find the angular velocity of the rod when the rod becomes horizontal 1 2 411 2q 3rED ma 3 3xCo ma 6Eo ma 2q A 2a q q 2a

spheres of radii r and r are touched and separated Calculate the ratio of their i Charges iii Self energy v Surface charge density ii Potential iv Electric field at the surface

Displacement current is same as Question Type Single Correct Type 1 2 conduction current due to flow of free electron 4 conduction current due to flow of positive ions conduction current due to flow of both 3 positive and negative free charge carriers is not a conduction current but is

31 The voltage of clouds is 4 x 106 V with respect to ground In a lightning strike lasting 100 ms a charge of 4 C is delivered to the ground The power of lightning strike is 1 160 MW 2 80 MW 3 20 MW

From NC The displacement of a charge Q in the electric field E e i e 3 ezk is r a bj The work done is 1 Q ae be 2 Q ae be 3 Q e 6 e2 4 Q 2 a b V

Four identical particles each of mass m and charge q are kept at the four corners of a square of length L The final velocity of these particles after setting them free will be Kq mL 2 1 5 4 Kq 4 2 1 35 1 35 1 2 3 NE 2 7 Kq mL 4 Zero From NCERT

Three charges Q q and q are placed at the vertices of a right angled isosceles triangle as shown The net electrostatic energy of the configuration is zero if Q is equal to 1 2 9 1 2 2q 2 2 3 2q 4 q

20 A 1 C charge is uniformly distributed on a spherical shell given by the equation x y 2 25 What will be the intensity of electric field at a point 1 1 2 1 5 N C 3 112 5 N C Two charged 2 45 N C 4 Zero

4 The ratio of electric potential due to a short electric dipole at point A whose position vector w r t centre of dipole makes 60 angle with direction of dipole moment to that at point B on axial position is Both points are at same distance from the center of the dipole 1 1 3 3 1 2 2 1 1 4 2 1

6270 From NCERI A charge of 10 e su is placed at a distance of 2 cm from a charge of 40 e s u and 4 cm from another charge of 20 esu The potential energy of the charge 10 e s u is in ergs 1 87 5 2 1125 3 150 4 250

The displacement of a charge Q in the electric field E e i ez ezk is r ai bj The work done is 1 Q ae be 2 Q ae be 3 Q e b e2 4 Q e a b

30 The diagram below shows equipotential lines in a region where there is a uniform electric field A proton is released from rest at the point marked with an O Which ONE of the following statements best describes the motion of the proton after its release OV IV 0 1 0 m 2 V 3 V A It will remain stationary at the point marked with an O to the right B It will move at a constant velocity of 1 0 ms C It will move at a constant velocity of 3 0 ms to the left D It will accelerate at 1 2 x 10 ms to the right E It will accelerate at 2 9 x 10 ms2 to the left