Electric Field and Potential Questions and Answers

Here written that Because iron is a conduct or so when we rub it then electrons move wi thin the conductor and did not become stati c on the other hand glass rod is an insulator and when we rub it get charge on its surfac e and act like a charged body But my questi on is that our body also a conducter so why don t the electrons in our roam inside of our body instead of losing

A particle of mass 2 kg and negatively charged is released form very large distance along the tunnel diametrically of uniformly positively charged spherical distribution as shown in figure it the speed at mouth of tunnel is 2 m s then find KE in Joule at centre Assume gravity free space

A particle of mass m has a charge q0 when it is at rest When the particle moves with s peed v the charge on the particle will beco me c is the velocity of light in vacuum 1 q0v c 2 q0c v 3 q0 01 12 21

A very long charged solid cylinder of radius a contains a uniform charge density p Dielectric constant of the material of the cylinder is k What will be the magnitude of electric field at a radial distance x r a from the axis of the cylinder A D EU A B P X Co X 2kEo B p C p Sca taket wit c X 2k 2080 Apie C p 2k 2360 D P X 2k

A charge Q is placed at the center of the line joining two point charges q and q as shown in the figure For system of three charges are equilibrium Then the ratio of Q and q is Q q 14 X X a 4 b 1 4 The forgo per unit charge is known as c 4 q d 1 4

20 A charge q moving in a staight line is accelerated by a potential difference V It enters a uniform magnetic field B perpendicular to its path Then the radius of the circular path in which it travels will be 2mV 982 2mV 98 mv V982 b 982 2mV d 982 mV

90 Electric flux will be maximum when a electric field and area are perpendicular to each other b electric field and area are parallel to each other c electric field and area are at an angle other than 0 and 90 d None of the above

A point charge q is placed at origin The electrostatic energy stored in the space around the point charge in various volumes as mentioned in listed in options below Choose the correct option s below A small cube with edge size a a r placed at r 0 0 has A energy B A small cube with edge size a a r placed at r 0 0 has C Energy stored in volume given by a x y z 4a is D Energy stored in volume given by a x y z 4a is q a 32 or4 q a 16 or 4 q 16 q 32 amount of amount of energy

12 A thin infinite uniformly charged plane sheet is given in the figure below Study the following statements I Electric field at P is equal to electric field at Q II Conducting thin sheet produces double electric field strength at P as compared to non conducting thin sheet III Gauss s law is not applicable to a charged thin conducting sheet Now choose the correct statement s a Only I c Both I and II b Only II d All of these

An electrical charge distribution is given by volume charge density p r ar 0 r R when r is the radial coordinate Find the electric flux due to this distribution through a closed cylindrical surface of radius R enclosing the above charge distribution Options 1 47 o aR 4 2 GR4

ECTRIC CHAR A small electric dipole is placed with its dipole moment directed along positive x axis The direction of electric field at a point 2 2 2 0 is 1 Along positive z axis 2 Along negative z axis 3 Along positive y axis V avis

An electron falls through a distance of 1 5 cm in a uniform electric field of magnitud 2 0 10 N C Fig a 111 A Calculate the time it takes to fall through this distance starting from rest

14 A point charge 1 nC is placed at 50 cm from the centre of a conducting shell of radius 20 cm having 3 nC charge There is a cavity in the solid sphere having a positive charge 2 nC Due to system of shell potential at point P AP 10 cm as shown in the figure is 2nC B 27

17 A half ring of radius r has a linear charge density The potential at the centre of the half ring is 2 1 480 2 2 4 or 2 3 A or 4 2 4 r 2

A nonconducting ring of radius R carries no NET charge Then Electric field intensity on the axis of ring is always zero Axial component of electric field intensity on the axis of ring is always zer Net electric field on the axis can have any finite value

We know that if charge is distributed on a body these charges interact to give a certain self energy to the body This self energy can be calculated in many ways One of the ways is to integrate the energy spread out in entire space in form of C electric field U We can assume an electron to be like a uniformly charged thin shell of radius ro having self energy Eo This energy has been estimated in nuclear reactions as 0 51 MeV From this we can find out an approximate radius of the electron at is the approximate radius of electron e 4 o Eo e 8 o Eo e 4 0E0 2 z 0E dv 2 A

ee charges q Q and Q are placed at the corners of an equilateral triangle of side 0 48 m as shown he case q 1 nC on top and Q 6 nC so in the triangle the bottom left particle has charge 6 nC while the bottom right particle has charge 6 nC what is the electric potential in the center of the trian 10 10 20

51 The electrostatic potential o of a spherical symmetrical system kept at origin as shown in the adjacent figure is given as Ro a Only 1 c Both I and II 9 4 or 9 4 TERO r R r Ro I Which of the following statement s is are incorrect I For spherical region r Ro total electrostatic energy stored is zero II Within r 2Ro total charge is q 2 III There will be no charge anywhere except at r Ro b Only II d I II and III

The dielectric constant D 10 15 10k t of medium 1 is 4 3 and the dielectric E constant of medium 2 is 2 6 for two infinite homogeneous isotropic dielectrics with E charge free interface Both meets at z 0 plane as shown in the figure For z20 the electric field is E 31 4 6k Calculate the electric displacement vector in medium 2 The figure is given below Medium 1 Medium 2 a D b c D 0 5 Z O 18i 24j 18k 4i 6 10k 10i 15j 10k 4i 6i 106

O electric flux O electrostatic O electric field lines O electric field Question 2 O electric field lines O electric field Question 2 If the distance between two charges is doubled the electrostatic force between the charges will between be four times less increase two times

A point charge q is placed in front of a thin conducting spherical shell of radius R at a distanc 2R from the center of sphere Mark the correct statement V stands for potential at point i A V VB A q 2R A R B B V V Vc VB C VA A D C 1 q 4 2R D V VB 1 q 4 3R ATE

8 Find the potential of the electrostatic field inside a cylinder of length 1 and radius if each end of the cylinder is grounded and the surface is charged to a potential uo

Density of a sphere of radius R with concentric spherical cavity of radius r x R then where x is distance from its centre and A B C D Column 199 If potential on its outer surface ap GR 81 bap GR 81 then c then b 14 11 from its centre dp GR 81 IM Potential at its inner surface Field on its surface Cap GR 81 Field at a distance then aa 1 RIN then d Y P s 0 Column 11 0 12 14 is given by p R

An electric dipole is situated in an electric field of uniform intensity E whose dipole moment is P and moment of inertia is I If the dipole is disturbed slightly from the equilibrium position then the angular frequency of its oscillations is 1 2 1 2 PE 1 PE 2 2 1 2 3 28 1 PE 1

Q2 The Figure shows a ring of radius R Charge is uniformly distributed along the ring The left black semicircle carries a positive charge 2Q and right white circle carries a negative charge Q What are the magnitude and direction of the electric field at center of the semicircle in unit vector notation Show details of your work Take R 10cm and Q 10nC X

A solid sphere carrying a uniformly distributed charge q within its volume rotates about a diameter 2r So that the speed on its equator is v The electric field at the outer surface of the sphere is 1 q 4T 1 2 3 4 9 47 3r 1 9 4T 22 1 2q 4 EO 2

10 A uniform right angled triangular lamina is placed on a horizontal floor which is not frictionless One of the acute angle of the lamina is as shown in the figure by the top view of the situation If FA and FB are the minimum forces required to rotate the lamina about stationary vertical axes through the vertices A and B respectively find the minimum force required to rotate the lamina about a stationary vertical axis through the vertex C A 0

4 Four charges equal to Q are placed at the four ccrners of a square and a charge q is at its centre the system is in equilibrium then the value of q is a 1 1 2 2 Q b 2 2 1 2 1 1 2 2 C d 10 1 2

If PR PL Pc denotes the average power dissipated per cycle in resistor inductor and capacitance of series LCR circuit respectively then O PL PC 0 O PL 0 Pc 0

A non conducting spherical shell of radius R having charge distribution q and q is released from rest on a horizontal non conducting rough surface as shown in figure in a horizontal electric field E The initial value of friction force so that the sphere does not slip is till

5 Derive the final equation first for every probler before plugging in the values given 6 Round off all answers to two decimal places T T3m15m 82 81 4 What 83 should be the of charge order force acting zero for 8 Zuc 83 Juc the total on it to

Four charges 2C 3C 4C and 5C respectively are placed at all the corners of a square Which of the following statements is true for the point of intersection of the diagonals Electric fields is zero but electric potential is non zero O Electric fields is non zero but electric potential is zero

An electric dipole is placed along the x axis at the origin O A point P is at a distance of 20 cm from this 75 origin such that OP makes an angle 3 with the x axis If the electric field at P makes an angle 8 with x axis the value of 0 would be

39 Two point charges 4q and q are fixed on the r axis at x d 2 and 2 d 2 respectively If the third point charge q is taken from the origin to z d along the semicircle as shown in the figure the energy of the charge will A Increase by C decrease by 29 3reod Aneod 4q 9 B Increase by D decrease by 24 1read 17 3rend

28 Two charged thin infinite plane sheets of uniform charge density o and o where lol lol intersect at the right angle Which of the following best represents the electric field lines for the system C I D

When current in a coil changes from 5 A to 2 A in 0 average voltage of 50 V is produced The self inductal of the coil is a 6H c 3H b d 0 67H 1 67 H

A point charge 1 nC is placed at 50 cm from the centre of a conducting shell of radius 20 cm having 3 nC charge There is a cavity in the solid sphere having a positive charge 2 nC Due to system of shell potential at point P AP 10 cm as shown in the figure is P B

Consider a postive point charge q fixed in space A second positive point charge q is moved from point C to point D such that point C is at a distance R from q and point D is at a distance 2R from q as shown in the figure The electric work WCD done on q as it is moved from C to D is R B 92 2R

A metallic sphere is given some charge Electric energy is stored A B C D Only inside the sphere Only outside the sphere Both inside and outside Neither inside nor outside

along CA F 20 10 5 N suspended by strings of equal lengths The strings m Problem 1 19 Two identical charged spheres an angle 30 with each other When suspended in al of density 800 kg m3 the angle remains the same W is the dielectric constant of the liquid The density Roorkee 1988 LLT 19 ach of the the material of the sphere is 1600 kg m 3 suched to The two spheres A and B each of weight Wa Blin each carrying charge 4 when suspended by strings gths come to rest so that the strings make a angle of 30 with each other Therefore each string w make an angle of 15 with the vertical Fig 1 27 S Using the equ

When a heater heated with the current of 5A with a resistance 6ohm and 10L water taken in a jar and heated the temperature of water is 10degree celcius then how much time will taken to rise temperature to 100degree the K of jar is 1000 A 30 B 40 C 50 D 60

35 Two charges q and 2q are placed on smooth table with a separation d Where should the third charge Q is to be clamped on the table such that the charges q and 2q remain at rest 1 2 1 d from 29 2 2d from q 3 2 1 d from q 4 2 1 d from q

4 It gets burst 26 Charges q 2q 4q 8q are placed along x axi at r 2r 4r 8r from origin respectively The n electric field at origin is 1 q 2 4 or a 2 4 2q 2 4 or q

2 A particle of mass m and charge q is thrown at a speed u against a uniform electric field E The distance it travelled before coming to rest will be 1 3 2mu qE mu 2qF 2 4 mu qE 4 mu gE

A particle of charge q and mass m moves in a circular orbit around a fixed point charge Q in a circle of radius r and time period T Which of the following may be correct 1 3 x 7 3 T2 3 2 x T3 2 4 2 x T3

23 Two identical metallic spherical shells A and B having charges 40 and 10Q are kept a certain distance apart A third identical uncharged sphere C is first placed in contact with sphere A and then with sphere B then spheres A and B are brought in contact and then separated Find the charge on the hores A and B All India 2011 al

The electric field in the space is given by E E xi y zk Consider a right circular cylindrical surface whose radius is a and height h as shown in the figure Now choose the correct option s A The electric flux through lower circular base is zero B The electric flux through upper circular top is ma hE C The electric flux through lateral surface is 2 hE D The total electric flux through cylindrical surface is 4ta hE Z

A thin rod of length 2 3R is charged uniformly with linear charge density 2 Another rod semicircular in shape and radius R is also charged with the same linear charge density 2 Now the rod is placed perpendicular to the plane of the semi circular ring in such a way that the mid point of the rod coincides with the centre of the semi circular ring Find the magnitude of the force experienced by the rod ptions 2 3k1 3k1 k2

Two charged objects have an attractive force of 0 0929 N If the distance separating the objects is quadrupled then what is the new force Hint Round your answer in four significant figure and you DO NOT need to write the unit

Sir How answer is given straight line 4 3 x4 29 The graph between magnitude of electric field due to a point charge as a function of inverse of square of distance from charge is 1 Hyperbola 3 Ellipse 2 Parabola 4 Straight line