Electric Field and Potential Questions and Answers

The electric field vector at point P a a a due to three uniformly charged infinite wires 1 2 and 3 kept the x y and z axes respectively as shown in shown in figure is Charge unit length of each wire is X Z A 3mega i i k

In a glass bulb filled with gaseous neon two metal plates are used as electrodes separated by a distance d 4 mm that is much smaller than the linear dimensions of the plates Ionization energy for neon atom is 21 5 eV average distance travelled by an electron between two consecutive collisions with neon atoms is 1 0 4 mm and charge on an electron is e 1 6 10 19 C How much potential difference between the electrodes should be applied to initiate a discharge process And End Eo

A solid spherical conductor of radius R has a spherical cavity inside it as shown in the figure 1 A point charge q is placed at the centre of cavity In second figure the cavity is irregular in shape and q is placed at same point in V V R q 7 The potential of the conductor in figure 1 is V and that in figure 2 is V then choose the CORRECT statement V 4 E 1 9 4 R 19 R R V depends on position of q inside cavity 2 V and V depend on the position of charge inside cavity 1 q

4 A charge of 17 7 x 104 C is distributed uniformly over a large sheet of area 200 m Calculate the electric field intensity at a distance of 20 cm from it in air If a charged particle of charge 2 0 x 10 C is placed at this point calculate the force of attraction between the particle and the plate 5 x 105 N C 1 N

There is a non conducting sphere of uniformly distributed charge density p insulated from surrounding There is a cavity inside the sphere as shown in figure P is the centre of sphere and C is centre of cavity Value of VA Ve is of the form where ko is constant Then value of ko will be VA and Ve are the electrostatic potential A and C It is given pa koto that PC a AB a 2 BC a 2 AB is parallel to PC and BC is perpendicular to PC fo 0 00

06 07 08 R 9 09 V decreases 10 V increases 11 V remains unchanged 12 13 Q 17 18 of 54 A solid spherical conductor of radius R has a spherical cavity inside it as shown in the figure 1 A point charge q is placed at the centre of cavity In second figure the cavity is irregular in shape and q is placed at same point it R 14 15 16 17 18 If the charge inside cavity in figure 1 is displaced by Ax away from the centre of sphere along the line joining the centres of sphere and cavity then choose the CORRECT statement 18

Number of electrons removed from a neutral metal sphere are 20 x 10 then this sphere is put in contact with a neutral sphere of double the radius then the charge on the bigger sphere is 1 32 C 3 32 C 264 C 3 4 64 C

2 A circular ring carries a uniformly distributed positive charge and lies in the xy plane with center at the origin of the coordinate system If at a point 0 0 z the electric field is E then which of the following graphs is correct a E Z Z 02 TD

from a distance 4 am A charged particle of charge q and mass mis projected with initial velocity Vo a from the fixed charge Q at an angle of a 60 with the line joining the charges in the figure It is found the the particle moves on an elliptical orbit with the charge Q at one of its foci The length of the semi major axis of the ellipse equals to a a 3 AND

There are two concentric conducting shells The potential of outer shell is 10 V and that of inner shell is 15 V If the outer shell is grounded the potential of inner shell becomes remains 1 25 V 3 10 V 2 15 V 4 5 V

Q A globe is fitted with identical charged particles of charge q on the equator at an angular separation of 300 The radius of globe is given to be R Find potentials at the north pole of globe B C D 12kq 2R 12kq R 24kq 2R 12kq an V k 22 R x R k 129 North pole IR 2 2 2

2 Find the electric potential of the conductor in the form of a circular loop of radius R and has a total charge Q The loop is enclosed in a grounded spherical shell and the radius is R where R R

Figure below shows a small sphere with mass 1 50 g hangs by a thread between two very large parallel vertical plates 5 00 cm apart The plates are insulating and have uniform surface charge densities a and o The charge on the sphere is q 8 90 x 10 6 C If the thread to remain at an angle of 30 0 with the vertical calculate a 30 0 5 00 cm the potential difference between the plates 8

All the charge particles each of magnitude q lie on the circumference of a ring of radius R as shown in the figure Find the magnitude of net electrostatic force acting on the charge particle P A 5 3 4 kq 2 3 R C 3 3 2 kq 3 R B D 3 3 2 kq 2 3 R 5 3 4 kq 4 3 R q 30 30 5 q 60 R 30 30 q P q

Shown in the figure is a spherical shell with inner radius a and outer radius b which is made of conducting material A point charge Q is placed at the centre of the shell and a total charge q is placed on the shell Charge is distributed on the surfaces as 1 q 2 b Question Type Single Correct Type a Q on the inner surface q on the outer surface Q on the inner surface q Q on the outer surface 0 on the inner surface a 0 on the

Problem 2 32 Two positive point charges qA and q masses m and m are at rest held together by a massless string of length a Now the string is cut and the particles fly off in opposite directions How fast is each one going when they are far apart

Total charge Q is uniformly spread along circumference of a fixed ring of radius R A small test charge q of mass m is kept at the centre of the ring and is given a gentle push small displacement along the axis of the ring Find the time period of the motion of charge q in second Given mass of test charge q is m Qq 6473 oR3

If 50 joule of work must be done to move an electric charge of 2 C from a point where the potential is 10 volt to another point where the potential is V volt then the value of V is 1 5 V 2 15 V 3 15 V 4 10 V

Some equipotential lines are as shown is fig E E and E3 are the electric fields at points 1 2 and 3 then fagurfa tarta E f 1 2 i 3 fa E E 2 2 11 60V 50V 40V30V 20V 70V A E E E3 B E E E3 C E E E E3 D E E Your Answer D E3

Two Concentric charged sphere of radi us R and 3R carry q and Q amount of ch arges Q q If two spheres are conne cted by a conducting wire What will be final distribution of charges on the two spheres

a 17 b 11 c 9 d 14 25 A proton is revolving on a circular path of radius 2 mm with frequency 10 Hz Magnetic dipole moment associated with proton is a 2 10 24 A m X c 3 10 20 A m b 4 x 10 24 A m d 6 x 10 20 A m

Read the assertion and reason carefully to mark the correct option out of the options given below Assertion A When a dielectric is placed in uniform electric field anywhere inside the dielectric the volume element AV has no net charge though it has net dipole moment Reason R The induced dipole moment is opposite to the direction of the external field If both assertion and reason are true and the reason is the correct explanation of the assertion If both assertion and reason are true but reason is not the correct explanation of the assertion If assertion is true but reason is false O If assertion is false but reason is true

Two concentric shells kept in air have radii Ra r They have similar charge and equal surfa charge density o The electrical potential at th common centre is 1 3 o R r Eo o R r 28 2 4 o R r Eo o R r 4

Three charges with magnitudes q 2q 3q are placed at the vertices of an equilateral triangle whose each side is of length a Only by changing the signs of charges we change the electrostatic energy of the configuration Then the energy gap between the most stable and most unstable configuration is 24 11009 12 112 25 11 18

A C power is transmitted from a power house at a high voltage as A B C the rate of transmission is faster at high voltages it is more economical due to less power loss power cannot be transmitted at low

harge Q is distributed on a small hollow conducting sphere radius r This sphere is kept inside a spherical cavity of radius r which is made inside a olid neutral conducting sphere of radius reas shown in the figure The total electrostatic energy of the system is IN d

19 A point charge q is placed at a distance r from the centre O of an uncharged spherical shell of inner radius R and outer radius 2R The electric potential at the centre of the shell will be a 1 1 The 4TEO r 2R c q 1 4 r 2R Conductor b 9 R q 4 or d None of these O 2R

32 Six charges are placed at the vertices of a regular hexagon as shown in the figure The electric field on to the plane of the figure at a distance of x a the line passing through point O and perpendicular from O is Qa TEOX 3 Q b Q TO Q 2Qa 3 a Q 3 Qa 3 c ba d zero

33 If an electron enters into a space between the plates of a parallel plate capacitor at an angle a with the plates and leaves at an angle to the plates The ratio of its kinetic energy while entering the capacitor to that while leaving will be a 16 c COS a cos B sin a 2 d cos B COS a sin B sin a 2

12 A conducting shell of radius R carries charge Q A point charge Q is placed at the centre The electric field E varies with distance r from the centre of the shell as IET a c Ex Me 11 R R r r b d E Et R R CO

3 Intensity and potential of a charge at point of r distance from it is E V respectively Medium of dielectric constant K is introduced Position R for which the potential intensity will be of earlier value 2 r K 1 2 r K 1 r K r K 1 2 3 r K r K 2 4 None of above

37 In the following figures which represents the variation of the electric field with distance from the centre of a uniformly charged non conducting spheres of radius R a 1 r2 E b E 1 r2 E pod 1 r2 Mu d 1 r2 R 1 r te

A circular path of 10 cm radius is imagined in a uniform electric field of field strength 10 V m such that its plane coincides with the plane of field lines as shown in the figure The modulus of ratio of work done in moving same charge in first quarter to third quarter is E Zero 1 1

44 An insulated ring of radius 4m having a charge 91 2 x 10 5C is uniformly distributed over it Another particle having charge q2 4 x 104 C is released from rest along its axis at a distance x 3m from its centre Mass of both ring and the particle is 1 kg each Neglect gravitational effects Ring is free to move Maximum speed of particle will be st a 4 4 m s b 3 1 m s c 5 2 m s d 6 1 m s

D3 5 A point charge of 0 25 C is located at r 0 and uniform surface charge densities are located as follows 2 mC m at r 1 cm and 0 6 mC m at r 1 8 cm Calculate D at a r 0 5 cm b r 1 5 cm c r 2 5 cm d What uniform surface charge density should be established at r 3 cm to cause D 0 at r 3 5 cm

23 A solid conducting sphere of radius 10 cm is enclosed by a thin metallic shell of radius 20 cm A charge q 20 C is given to the inner sphere Find the heat generated in the process the inner sphere is connected to the shell by a conducting wire a 12 J b 9 J c 24 J d zero

A small coin is resting on the bottom of a beaker filled with 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 2007 100 BET 4 cm K 3 cm coin a 2 4 108 m s c 1 2 108 m s b 3 0 108 m s d 1 8 108 m s 47 48 40

7 Point charges q and q are located at the vertices of a square with diagonals 21 as shown in Fig 3 1 Find the magnitude of the electric field strength at a point located symmetrically with respect to the vertices of the square at a distance x from its centre 8 A thin half ring of radius R 20 cm is q q 21 Fig 3 1 q q

0 The kinetic energy of the system of charges left free after long time is 1 Zero 2 Cannot be produced 3 3 kq a u 4 kq a AR What is the

83 A large sheet carries uniform surface charge density o A rod of length 21 has a linear charge density on one half and on the second half The rod is hinged at mid point O and makes an angle 0 with the normal to the sheet The maximum torque experienced by the rod is if 0 is variable a ON 280 02 EO c b 02 280 ON En d

99 A charge distribution that is spherically symmetric but radially not uniform produce an electric field of magnitude E kra radially outward from the centre of the sphere here k is a positive constant and r is the radial distance from the centre If p be the volume charge density at a distance r from the centre then a pa 1 b px 1 c pa 2a d pa 2 2 px

the identical charges each of 1 0 c are placed at the corners of an equilateral triangle of side 10cm the electric field intensity at the centre of triangle is O270x10 5 n c O27x10 4 n c O 27x10 5 n c O 2 7x10 4 n c

89 A point charge q 30 C is kept at a distance 3R from the center of a neutral conducting sphere radius R as shown in the figure When the switch S is closed the amount of charge flowing from the sphere into the ground will be a 5 C c 10 C S 3R b 10 C d zero the and the inc a 93 Ir th Te

9 An infinite number of identically charged bodies are kept along the x axis at points 0 1m 2m 4m 8m 16m and so on All other charges repel the charge at the origin with a force of1 2N Find the magnitude of each charge Ans 10 c

A charge is uniformly distributed in a spherical volum of radius R The electric field at distance r r R from its centre is proportional to r 1 r 2

A particle A of charge q is placed near a uniformly charged infinite plane thin sheet with surface charge density o then it experiences a force F When this particle is placed near a metal plate with surface charge density of one surface o then it experiences a F force F2 Then 1 2 12 2 3 is equal to

A point charge q0 moves from point A to B in semicircular path of diameter 2a then to point C in a semicircular path of diameter a and finally to point D in a circular path of radius a 2 tracing an angle ZCOD of 60 as shown Point A is distance 6a apart from infinitely long wire with its centre at origin having linear charge density 2 All circular paths and wire are in the same xy plane Length of the wire 6a Minimum work done to move the charge from A to D is B 60 T 6a a 2a A

A small charged pith ball moves on a smooth table towards an oppositely charged metal ball that is held place on the table Which of the curves shown in figur most realistically reflects the speed v of the pith ball a function of the distance r between the balls Initial distance between them is R V V R R r

An electric dipole consists of two electric charges of 1 0 C and 1 0 C separated by a distance of 2 0 cm The dipole is placed in an external electric field of 1 0 105 N C The maximum torque on the dipole is 0 2 x 10 3 Nm 1 0 10 3 Nm 2 0 10 3 Nm 4 0 10 Nm

A parallel plate capacitor is connecte from a cell and then isolated from it Two dielectric slabs of dielectric constant K and 2K are now introduced in the region between upper half and lower half of the plate as shown in Figure The electric field intensity in upper half of dielectric is E and lower half is E2 then A E 2E B K E 2K E 2 Electrostatic potential energy of upper half is less that of lower half C Induced charges on both slabs are same Charge distribution on the plates remains same after insertion dielectric