Q.1 A uniform electric field of 10N/C exists in the vertically downward direction. Find the increase in the electric potential as one goes up through a height of 50cm.
[Ans. 5V]
Q.2 12J of work has to be done against the existing electric field to take charge of 0.01C from A to B. find the potential difference VB-VA.
[Ans. 1200V]
Q.3 Two charges 4 x 10-9C and -3x10-9C are located 0.1m apart. At what point on the line joining the charges is the electric potential zero? Take potential at infinity to be zero.
[Ans. 0.057m from first charge]
Q.4 Two charged particles having equal charges of 2 x 10-5C each, are brought from infinity to within a separation of 10cm. find the increase in electric potential energy during the process.
[Ans. 36J]
Q.5 Electric field due to a point charge s 20N/C and the electric potential at that point is 10J/C. Calculate the distance of point from the charge and the magnitude of the charge.
[Ans. 0.5m, 5.56x10-10C]
Q.6 Calculate the electric potential at the surface of gold nucleus. Given the radius of nucleus is 6.6x10-15m.
[Ans. 1.72x107V]
Q.7 A electric field E = Ax 
exists in space, where A = 10V/m2. Take potential at (10m, 20m) to be zero. Find the potential at the origin.
exists in space, where A = 10V/m2. Take potential at (10m, 20m) to be zero. Find the potential at the origin.
[Ans. 500V]
Q.8 Two equal charges of 2 x 10-7C each, are held fixed at a separation of 20cm. a third charge of equal magnitude is placed midway between the two charges. It is now moved to a point 20cm from both the charges. How much work is done by the electric field during the process?
[Ans. 3.6x10-3J]
Q.9 Three point charges –q, Q and –q are placed at equal distances on a straight line. If the total potential energy of the system is zero, then what is the ratio of Q:q?
[Ans. 1:4]
Q.10 An alpha particle with KE 10MeV is heading towards a stationary tin nucleus of atomic mass 50. Calculate the distance of closest approach.
[Ans. 14.4x10-15m]
Q.11 Two particles each having equal masses of 5gm each and opposite charges 4x10-5C and -4x10-5C. They are released from rest with a separation of 1m between them. Find the speed of particles when the separation is reduced to 50cm.
[Ans. 54m/s for each particle]
Q.12 Two identical particles, each having a charge of 2 x 10-4C and mass of 10gm are kept at a separation of 10cm and then released. What would be the speeds of the particles when the separation becomes large?
[Ans. 600m/s]
Q.13 The kinetic energy of charged particles decreases by 10J as it moves from a potential of 100V to a point at potential of 200V. find the charge on the particle.
[Ans. 0.1C]
Q.14 A sphere is centered at the origin has radius of 0.200m. A -5μC point charge in on the x axis at x=0.300m. the net electric flux through the sphere is 360N/m2. What is the total charge inside the sphere?
[Ans. 3.19nC]
Q.15 A 9.6μC charge is placed at the center of the cube with sides of length 0.500m. [a] what is the electric flux through one of the six faces of the cube? How would the answer in part [a] change if the sides are of length 0.250m.
[Ans. 1.81x105 Nm2/C, no change]
Q.16 A very long uniform line of charge has charge per unit length 4.8μC/m and lies along x axis. A second long uniform line of charge has charge per unit length -2.4μC/m and is parallel to x axis at y=0.40m. What is the net electric flux at the following points [a] y=0.2m and [b] y=0.6m?
[Ans. 6.47x105N/C along y, 7.2 x104N/C along –y]
Q.17 Two insulating spheres with radius 0.080m are separated by a center to center distance of 0.5m. one sphere has a net charge of -1.8μC and the other has charge of 3.8μC. The charge is uniformly distributed within volume of each sphere. What is the electric field midway between the spheres?
[Ans. 8.06x105 along –ve sphere]
Q.18 An insulating sphere with radius 0.220m has charge distributed uniformly through its volume. What must be the total charge on the sphere if the electric field 0.110m from the center of sphere is 950N/C?
[Ans. 10.2nC]
Q.19 A cube of side 16cm is lying with its base along x axis. Electric field along x axis is given by 500√x, whereas the components of field along z axis and y axis are zero. What is the flux through the cube and also charge in the cube if left face of the cube is at (16, 0,0) cm.
[Ans. 1.88x10-11C, 2.12Nm2/C]
Q.20 Uniform electric field E for negative x is given as -100 N/C and for positive x as 100 N/C. a cylinder of length 30cm has its axis along x axis and with its center at (0,0,0). Radius of the cylinder if 10cm. find flux through each face, curved surface as well as net flux through the cylinder. Also find charge in the cylinder.
N/C and for positive x as 100 N/C. a cylinder of length 30cm has its axis along x axis and with its center at (0,0,0). Radius of the cylinder if 10cm. find flux through each face, curved surface as well as net flux through the cylinder. Also find charge in the cylinder.
[Ans. φC=0, φ = 6.28Nm2/C, 5.68x10-11C]
Q.21 Electric field components due to charge inside the cube of side 0.1m placed at a distance of 0.1m from the origin is Ex=αx where α = 500N/cm and Ey=0, Ez=0. Calculate the [a] flux through the cube [b] the charge inside the cube.
[Ans. -40x10-2Nm2/C, -3.54x10-12C]
Q.22 A uniformly charged conducting sphere of radius 1.2m has surface charge density of 16μC/m2. Find [a] the charge on the sphere [b] the total electric flux leaving the surface of the sphere.
[Ans. 2.9x10-4C, 3.28x107Nm2/C]
Q.23 A particle having a charge of 1.6x10-19C enters midway between the plates of parallel plate capacitor. The initial velocity of particle is parallel to the plates. A potential difference of 300V is applied to the capacitor plates. If the length of capacitor plates is 10cm and they are separated by 2cm. calculate the greatest initial velocity for which the particle will not be able to come out of the plates.
[Ans. 104m/s]
Q.24 A charge q of mass m is projected with speed V towards another stationary particle of same mass and charge initially at rest. Find the distance of closest approach of the two particles?
[Ans. 4kq2/mv2]
Q.25 A particle of charge 3 x 10-9C is in a uniform field directed towards left. It is released from rest and moves a distance of 5cm after which the kinetic energy is found to 4.5x10-5J. what work was done by electrical force [b] what is the magnitude of the electric field? [c] What is potential energy of starting point w.r.t end point?
[Ans, 4.5x10-5J, 3x105N/C, 1.5x104V]
Q.26 There is infinite chain of charges q and –q the distance between the neighboring charges is equal to a. what is the interaction energy of each charge with all other charges
[Ans. -2
]
]
Q.27 A ring of radius R having two charges q and 2q distributed on its two half parts. Find the electric potential on the axis at a distance 2√2R from its center.
[Ans. 
]
]
Q.28 Two positive charges each of magnitude q are placed on the y axis at points (0,a) and (0,-a). If a positively charged particle of charge q0 and mass m is slightly displaced from origin in direction of negative x axis. [a] what will be its speed at infinity? [b] if a particle is projected towards the left along the x axis from a point at a large distance on the right of origin with velocity half of that acquired in part [a], at what distance from origin will it come to rest?
[Ans. v= 
, (√15 a, 0)]
, (√15 a, 0)]
Q.29 Two electric charge q and -2q are placed distance 6m apart. On a horizontal plane. Find the locus of a point on this plane where the potential has a value zero.
[Ans. the locus of point P is a circle of radius 4m with center at (-2,0)]
Q.30 A spherical drop has diameter 2mm and is given a charge of 5 x 10-6esu. [a] What is the potential at the surface of the cam? [b] if two such drops coalesce to form a single drop, what is potential at the surface of drop so formed?
[Ans. 23.8mV]
Q.31 A charge Q is distributed over two concentric hollow spheres of radii r and R [>r] such that the surface charge densities are equal. Find the potential at the common center.
[Ans. 
]
]
Q.32 A circular ring of radius R with uniform positive charge density λ per unit length is located in y-z plane with its center at the origin O. a particle of mass m and positive charge q is projected from point P(√3 R, 0,0) on the positive x axis towards O, with initial speed v. find the smallest value of v so that particle doesn’t return to P.
[Ans. vmin=
]
]
Q.33 Three charges q, 2q and 8q are to be placed on a 9cm straight line. Find the position where the charges should be placed to that the potential energy of the system is minimum. In this position what is the electric field at the position of charge q due to the other two charges?
[Ans. q at a distance of 3cm from 2q between two charges, E=0]
Q.34 Three point charges 0.1C each are located at the corners of equilateral triangle of side L=1m. If the system is supplied energy at the rate of 1kW, how much time would be required to move one of the charges on to the midpoint of line joining other two charges.
[Ans. 50 hr]
Q.35 The distance between the two plates of oscilloscope is 1cm and potential difference 1200V between them. If an electron of energy 2000eV enter at right angle to the field, what will be its deflection if the plates are 1.5cm long?
[Ans. 3.375mm]
Q.36 A charge Q coulomb is distributed over a spherical volume of radius R m. obtain an expression for energy of the system.
[Ans. U = 
]
]
Q.37 A radioactive source in the form of metal sphere of radius 10-2m emits beta particles at a rate of 5 x 1010 particles per second. The source is electrically insulated. How long will it take for potential to be raised by 2 volt assuming 40% of emitted beta particles escape the source?
[Ans. 700μs]
Q.38 A solid conducting sphere having a charge Q surrounded by an uncharged concentric conducting hollow spherical shell. Let the potential difference between the surface of solid sphere and shell is V. what will be the new potential difference if shell is given charge -3Q?
[Ans. V]
Q.39 Three concentric metallic spheres A, B and C have radius a,b and c (a<b<c) have surface charge densities σ,-σ and σ respectively. If shells A and C are at the same potential, find relation between a, b and c.
[Ans. a+b =c]
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