Electric Field and Potential Questions and Answers

Charge Q and 2Q are distributed uniformly on surface of two concentric spherical shells of radii R and 2R respectively as shown in the figure Select correct alternative s A the total electrostatic energy stored in the system is Q 8 R B electrostatic energy in the space between two shells is C electrostatic energy stored outside the system is Q 16 R Q 2 R D electrostatic energy in space between two shells is zero 2R 2Q R

The potential gradient along the length of uniform wire is 10 Vm The length of the wire is 1 m What is the potential difference across two points on the wire separated by 25 cm A 2 5 V B 5 0 V C 7 5 V D 10 V

Q Analyse the case of electrostatic shielding and answer the following questions i Draw the electric field lines when a charge is kept in metal cavity What will be affect on electric field lines when a charge is kept outside

Four non conducting wires each with mass m and length I are joined to form a square They are being charged with charge per unit length or as shown in the figure Initially the square is kept is xy plane and there exist uniform electric field E along z direction If the square is released from rest then it s maximum angular speed will be p 4 3 2EX AY 2 m value of p is OE

P I O Vpg 0 O A sphere carries a total charge which is negative and distributed uniformly on the surface Consider the potential difference Veg Vp Vo for the points indicated in the figure above Which of the following statements is true about that potential difference Vpg 2 Vpg Vpg 0 Vpg 0 not enough information to tell

A body having specific charge 8 C g is resting on a frictionless plane at a distance 10 cm from the wall as shown in the figure It starts moving towards the wall when a uniform electric field of 100 V m is applied horizontally towards the wall If the collision of the body with the wall is perfectly elastic then the time period of the motion will be S Body 100 V m

An object with charge q 2 C starts in a region at an electric potential of 10 V and then is moved to a region at 20V It then continues on to a region at 25 V and is brought to rest What is the net change in the object s electric potential energy across this entire process A B C D E 10 J 20 J 30 J 40 J 50 J

10 A small coin is resting on the bottom of a filled with a liquid A ray of light from the coin travels upto the surface of the liquid and moves along its surface How fast is the light travelling in the liquid 3 cm 4 cm coin 1 1 2 x 108 m s 3 1 3 x 108 m s AIPMT Prelims 2007 2 1 8 x 108 m s 4 3 0 108 m s

0 A thick shell with inner radius R and outer radius 3R has uniform density p c m It has a spherical cavity of radius R as shown in the figure The electric field at the centre O of the cavity is SHOPE bellatusal

13 Tow charges q and 2q are placed along the x axis in front of a grounded infinite conducting plane as shown in the figure They are located respectively at a distance of 0 5 m and 1 5 m from the plane The force acting on the charge q is 1 A 4TTE0 C 1 7q 4 2 1 q 4TE0 B 29 2q D 1 q 4 E 2

4nC are placed at the vertices of a square ABCD 8 Charges 3nC 1nC 2nC and respectively Find the work done to move the charge at D to the centre of the square if the side of the square is 2m

Two metallic spheres of radii a and b are separated by a distance d as shown in figure the capacity of the system is assuming d is very large in comparison to a and b az Options 4RE 1 a 1 b 2 d 2TE 1 a 1 b 1 d

A conductor having uniform linear charge denisty is placed in circular form in 3 quadrants with different polarities as shown in the figure Let E be the electric field at O Then the angle made by E with the line along y axis is YA 1 tan 3 tan 1 2 X X X R 2 tan 1 4 none

Three concentric conducting spherical shells A B and C of radii R 2R and 3R respectively carry some charge on them The potential at the centre is 50V and that of middle and outer shells is 20V and 10V respectively If q 9 and q are charges on the shells A B and C respectively then 6q 3q 3q is A 3000fv R B 1200fv R C 1800fv R D 1000fv R

1 In the above arrangement the ring can slide on the frictionless circular wire frame of radius a A a 2 charge Q is fixed at a distance from the cen tre O The minimum speed which must be given to the ring so that it can complete the circle is 3 kQq ma Dorox kQq 2 AV m q 4 3kQq ma 8kQq

positive 8 A point own in isolated conducting sphere figure The electric field is best given by q q q q Figure i i ii iii as iv b Figure ii

ii A point charge q 2 C is placed at origin point O The electric field in SI units at a point P whose coordinates are 0 5 0 m is a 7 2 x 104 b 7 2 104 672 104 104 9 10 C A 0 1 m 92 5 C B

4T E d 1 Consider a thin spherical shell of radius R consisting of uniform surface charge density o Th electric field at a point situated at a distance x x R from its centre is a inversely proportional to o c directly proportional to R b directly proportional to d inversely proportional to x it in a uniform elect

Two thin conducting shells of radii R and 2R are shown in figure The outer shell carries a charge Q and inner shell is neutral Choose the CORRECT option s H A With switch S open potential of inner sphere is same as that of point at distance 3R from centre 2 B When switch S is closed potential of inner sphere is non zero C With switch S closed charge on inner sphere is Q D With switch S closed charge on inner sphere is Q

4 There is spherical symmetric charge distribution around origin The electrostatic potential in Volts at a distance r from origin is given as V Kr where K is a 2 positive constant The slope of tangent to density vs r graph at rm is r Kv The find value of r

Charge Q coulombs is uniformly distributed throughout the volume of a solid hemisphere of radius R metres Then the potential at centre O of the hemisphere in volts is R O k

Two concentric spherical metal shells have radii R and 2R respectively The inner shell has charge Q and the outer shell has charge 2Q Potential at the centre of the combination is V 1 Now the outer shell is grounded and potential at the centre becomes V Find the value of V V O O Q 16TER Q 2 ER Q Ara P

Consider a rectangular prism with cross section of a right angled triangle as shown Co ordinates of vertices are A B C D and E are 2 0 0 2 2 0 0 2 2 0 0 2 and o 2 0 respectively There exists an electric field xi 2y k N C everywhere If charge enclosed by the prism is N then find the value of N ZD AY B A X Correct opower 02

a spherical shell of radius a has a surface charge density of ps find the electric field at the midpoint and a distance a from the surface a find the work done to bring a unit point charge from a to the center

charge distribution is given by V x y z 1 2 0 V 1 3 V 1 2 3V 3 where V is the potential at the origin and d is a distance Graph of electric field as a function of position is given as 2V d 1 2V d E 0 1 0 E 2V d 0 1 2 for x d E for d x 0 for 0 x d for x d x d x d x d

Find the electric field strength at 2 meters from the 5 millicoulomb charge q 5 mC 2m calculate the electric field here T Find the force on an proton placed 2 meters from the 5 millicoulomb charge in the problem above

14 A solid spherical conducting shell has inner radius a and outer radius 2a At the center of the shell a point charge Q is located What must the charge of the shell be in order for the charge density on the inner and outer surfaces of the shell to be exactly equal 1 5Q Q B 2a B 2 3Q 3 4Q 4 4Q

55 A two wire d c distributer supplies the following loads 20 50 Load amp Distant from Supply end metres 30 100 end is a 244V 80 200 The resistance of the distributer is 0 000152 per conductor per metre If the supply end voltage is 250V the voltage at the tapping point nearest to the sup b 246 6V c 248 2V 50 300 d 243V

2 Figure shows two equipotential lines in x y plane for an electric field The scales are marked The x component E and y component E of the electric field in the space between these equipotential lines are respectively y cm 3 2 1 0 0 2 4 1 100 V m 200 V m 2 100 V m 200 V m 3 200 V m 100 V m 4 200 V m 100 V m 6 2V 4V x cm

Three equal charges are placed at the corners of an equilateral triangle Which of the graphs below correctly depicts the equally spaced equipotential surfaces in the plane of the triangle All graphs have the same scale 1 3 8 10123 3 2 1 0 1 2 3 2 4 3 2 1 0 1 2 3 08 3 2 1 0 1 2 3

Eight identical charges of magnitude 1 C each are placed at corners of a cube of side 10 cm If a charge 1 C is placed at the centre of the cube the electric potential energy that can be associated with this charge is 12 3 25 1 3 6 3 J 2 4 6 3 J 25 4 3 J

Condition s for a charged particle to a line of force is are that it is released from rest the electric field is uniform its charge is positive a only a b simultaneously a b c simultaneously a b C 1 2 3

Three point charges are kept at points A 0 4a 0 0 0 and B 0 4a as shown in the figure A B C D A 0 4a 45Q 975Q A positive charge 8 of all four point charges to be zero 5Q X P 3a 0 5 0 4a B 3Q Work was done on the external agent who assembled these charges in moving them from infinity to the point The electric field at point P is E Ex E then Ex is negative and Ey is positive The electric field at point P is Ei E then both Ex and E are negative has to be put at point P to make the potential energy of system

2 The charge of an electron is 1 6 x 10 19 C How many electrons strike the screen of a cathode ray tube each second when the beam current is 16 mA a 10 7 C 10 19 b 10 9 d 10 7

42 ABC is an equilateral triangle with O as its centre F F2 and F represent three forces acting along the sides AB BC and AC respectively If the total torque about O is zero then the 70 magnitude of F3 is a F F b F F F F 2 d 2 F F c HAGE 1 8 B TH C R 12 which a that the is equal 4 a 12 c

Two small balls each of mass 8 5 g are attached to silk threads 80 cm long which are in turn tied to the same point on the ceiling as shown below When the balls are given the same charge Q the threads hang at 5 0 to the vertical as shown below What is the magnitude of Q How do the signs of the two charges compare Hint The magnitude of Qis chargo 5 0 C and the two charges carry Select an answer sign of

14 A straight current carrying conductor is kept along the axis of circular loop carrying current The force exerted by the straight conductor on the loop is O zero O 1 point perpendicular to the plane of the loop in the plane of the loop away from the centre in the plane of the loop towards the centre

55 The electric field intensity at P an shown arrangement are in the ratio 3q 1 1 2 2 2 1 3 1 1 4 43 2r Fig Hollow concentric shell

A circuit has section AB as shown in figure If the charge on each capacitor is 10 C then potential difference VA V is A F 1 F 15 V 3 10 V H 10 V 2 F 2 5 V 4 10 V FB

2b of the charge Q on a tiny sphere a fraction f is to be transferred to a second nearby sphere The spheres can be treated as particles a What value of f maximizes the magnitude F of the electrostatic force between the two spheres What are the b smaller and c larger values of f that put F at half the maximum magnitude

E maximum 4a A disk of radius 2 5 cm has a surface charge density of 5 3 C m on its upper face What is the magnitude o electric field produced by the disk at a point on its central axis at distance z 12 cm from the disk

6a A charge distribution that is spherically symmetric but not uniform radially produces an electric field of magnitude E K directed radially outward from the center of the sphere Here r is the radial distance from that center and Kis a constant What is the volume density of the charge distribution

In the figure below the particles have charges q 92 200 nC and q3 94 205 nC and distance a 6 0 cm Assume that the x axis is to the right and the y axis is up along the page a a What is the x component of the net electrostatic force on particle 3 IN b What is the y component of the net electrostatic force on particle 3 N

1b A nonconducting spherical shell with an inner radius of 4 0 cm and an outer radius of 6 0 cm has charge spread nonuniformly through its volume between its inner and outer surfaces The volume charge density p is the charge per unit volume with the unit coulomb per cubic meter For this shell p b r where r is the distance in meters from the center of the shell and b 3 0 p C m What is the net charge in the shell

la Of the charge Q initially on a tiny sphere a portion q is to be transferred to a second nearby sphere Both spheres can be treated as particles For what value of q Q will the electrostatic force between the two spheres be maximized

A cube of 3 8 m edge is placed in a non uniform electric field in N C given by Ex 2 x and Ey 3 y as shown in figure 3 Calculate the elecric flux in N m2 C2 of the electric field through the face F perpendicular the y axis

3b Charge is uniformly distributed around a ring of radius R 2 40 cm and the resulting electric field magnitude E is measured along the ring s central axis perpendicular to the plane of the ring At what distance from the ring s center is E maximum

What are the b smaller and c larger values of f that put F at half the maximum magnitude 3a What is the magnitude of a point charge whose electric field 50 cm away has the magnitude 2 0 N C 3b Charge is uniformly distributed around a ring of radius R 2 40 cm and the resulting electric field mag

the shell and b 3 0 C m What is the net charge in the shell 2a How many electrons would have to be removed from a coin to leave it with a charge of 1 0 x 10 2b of the charge 0 on a tiny sphere a fraction C

An electron starting from rest accelerates uniformly and moves through a distance of 0 64 m in 0 015 s The magnitude of the electric field in which the electron moves is in N C A 1 32 x 10 8 B 4 8 x 10 10 C 1 6 10 8 D 3 2 x 10 8