Test-2 (On Line)
Extra Questions For Practice
BOARD LEVEL QUESTIONS ON ELECTROSTATICS-1
Q.1
How many electrons must be removed from a piece of metal to give it a positive charge of 1.010-7 C?
Ans: 6.25×1011
Q.2
Calculate the total positive or negative charge on a 3.11 g copper penny. Given Avogadro’s number = 6.023×1023 per gram mole; for copper, atomic charge = 29 and atomic mass = 63.5.
Ans: ±1.37×105 C
Q.3
How far apart two protons be if the electrstatic force exerted by one on the other is equal to weight of the electron?
Ans: 5.11 m
Q.4
Two equal charges of +25 mC are placed 1 m apart. A test charge of +2 mC placed midway between them. Calculate force exerted by each charge and the net force on the test charge.
Ans: 1.8 N, Zero
Q.5
Two free point charges +4 e and +e are at a distance a apart. Where should a third point charge be placed between them so that the entire system is in equilibrium? What will be the magnitude and sign of q?
Ans: q=at a distance from the charge +4e
Q.6
Two electrons and a positive charge q are held along a straight line. At what position and for what value of q will the system be in equilibrium? check whether it is stable, unstable or neutral equilibrium:
Ans. At the centre of the line joining the charges, ¼ of each charge in magnitude, unstable
Q.7
Two equally charged particles, held 3.2×10-3 m apart, are released from rest. The initial acceleration of the first particle is observed to be 7.0 m/s2 and that of the second to be 0.9 m/s2. If the mass of the first particle is 6.3×10-7 kg, what are (a) the mass of the second particle and (b) the magnitude of the charge of each particle?
Ans: (a) 4.9×10-7 kg (b) 7.1×10-11 C
Q.8
four point charges qA=2mC, qB= -5mC, qC = 2mC and qD = -5mC are located at the corners of a square ABCD of side 10 cm. What is the force on the charge of 1mC placed at the centre of the square?
Ans: Zero
Q.9
Two small spheres each of mass 10-6 kg are suspended from a point by sild threads 50 cm long. They are equally charged and repel each other to a distance 20 cm apart. Calculate charge on each. Take g=9.8 ms-2
Ans: 2.98×10-9
Q.10
Two point charges q2=3´10-6 C and q1=5´10-6 C are located at (3,5,1) and (1,3,2) m. Find Using vector form of coulomb’s law.
Ans: = – (5×10-3)(2) N
Q.11
Two opposite corners of a square carry Q charge each and the other two opposite corners of the same square carry q charge each. If the resultant force on q is zero, how are Q and q related?
Ans: q= -2Ö2 Q
Q.12
Equal charges each of 20 m C are placed at x=0, 2, 4, 8, 16 cm on X-axis. Find the force experienced by the charge at x = 2 cm.
Ans: 1.184×103 N
Q.13
Two similarly and equally charged identical metal spheres A and B repel each other with a force of 2´10-5 N. a third identical, uncharged sphere C is touched with A and then placed at the mid-point between A and B. What is the net electric force on C?
Ans: 2×10-5 N towards A
Q.14
Two pieces of copper, each weighing 0.01 kg are placed at a distance of 0.1 m from each other. One electron from per 1000 atoms of one piece is transferred to other piece of copper. What will be the coulomb force between two pieces after the transfer of electrons? Atomic weight of copper is 63.5 g/mole. Avogadro’s number = 6x1023/gram mole.
Ans: 2.06×1014 N
Q.15
A particle of mass m and carrying charge -q1 starts moving around a fixed charge +q2 along a circular path of radius r. Prove that period of
Q.16
An infinite number of charges each equal to 4mC are placed along x-axis at x= 1m, x = 2 m, x = 4 m, x = 8 m and so on. Find the total force on a charge of 1 C placed at the origin.
Ans: 4.8×104 N
Q.17
Two identical helium filled balloons A and B fastened to a weight of 5 gram by threads float in equilibrium as shown in Fig. Calculate the charge on each balloon, assuming that they carry equal charges.
Ans: ±5.6×10-7 C
Q.18
Four particles, each having a charge q are placed on the four corners A,B,C,D of a regular pentagon ABCDE. the distance of each former from the centre is a. Find the electric field at the centre of the pentagon.
Ans:q/4pÎ0a2, along OE
Q.19
A water droplet of radius 1 micron in Millikan oil drop apparatus is first held stationary under the influence of an electric field of intensity 5.1×104 NC-1. How many excess electrons does it carry? Take e = 1.6×10-19 C, g = 9.8 ms-2 and density of water = 103 kg m-3.
Ans: 5
Q.20
A particle of mass m and charge q is thrown at a speed u against a uniform electric field E. How much distance will it travel before coming to momentary rest?
Ans: m u2 / 2qE
Q.21
Eight identical point charges of q coulomb each are placed at the corners of a cube of each side 0.1m. Calculate electric field at the centre of the cube. Calculate the field at the centee when one of the corner charges is removed.
Ans: Zero; 1.2×10-12 q NC-1 towards the corner without charge
Q.22
Two charges ±10 mC are held 5 mm apart. Calculate the dipole moment. What is electric field intensity due to this dipole at a distance of 15 cm from the centre of the dipole on the axial line of the dipole.
Ans: 5×10-8 C-m
Q.23
An electric dipole, when held at 30° with respect to a uniform electric field of 104NC-1 experiences a torque of 9×10-26 N-m. Calculate dipole moment of the dipole.
Ans: 1.8×10-29 C-m
Q.24
One HCl molecule has a dipole moment of 3.4×10-30 C-m. Calculate the maximum value of the torque acting on it in a uniform electric field of 2.5×105 N/C.
Ans: 8.5×10-25 N-m
Q.25
An electric dipole consists of charges +2 e and –2 e separated by 0.78 nm. It is in an electric field of strength 3.4×106 N/C. Calculate the magnitude of the torque on the dipole when the dipole when the dipole moment is (a) parallel to (b) perpendicular to, and (c) antiparallel to the electric field.
Ans: (a) Zero (b) 8.5×10-22 Nm (c) Zero
Q.26
A molecule of a substance has permanent electric dipole moment equal to 10-29 C-m. A mole of this substance is polarized (at low temperature) by applying a strong electrostatic field of magnitude 106 /m. The direction of the field is suddenly changed by an angle of 60°. Estimate the heat released by the substance in aligning its dipoles along the new direction of the field. for simplicity assume 100% polarization of the sample.
Ans: 3.012 J
Q.27
An electron moves in a vertical plane with a speed of 1.41×107 ms-1 and enters a region where there is a uniform electric field of 3500 NC-1, directed downwards. Find the co-ordinates of the electron 5×10-8 s after it passes through the point of entry along a course directed at an angle of 30° below the horizontal.
Ans: 0.61 m and 0.42 m
Q.28
Two charges of -4 mC and + mC are placed at the points A(1,0,4) and B(2, -1, 5) located in an electric field =0.20 î V/cm. Calculate the torque acting on the dipole.
Ans: 1.131×10-4 N-m
Q.29
Two point masses, m each carrying charges –q and +q are attached to the ends of a massless rigid non conducting rod of length l. The arrangement is placed in a uniform electric field such that the rod makes a small angle q=5° with the field direction. Show that the minimum time needed by the rod to align itself along the field (after it is set free) is t = .
Q.30
A rectangular surface of sides 10 cm and 15 cm is placed inside a uniform electric field of 25Vm-1, such that normal to the surface makes an angle of 60° with the direction of electric field. Find the flux of electric field through the rectangular surface.
Ans: 0.1875 Nm2 C-1
Q.31
A large plane sheet of charge having surface charge density 5×10-6 Cm-2 lies in XY plane. find the electric flux through a circular area of radius 0.1 m, if the normal to the circular area makes an angle of 60° with the Z-axis.
Ans: 4.44×103 C-1
Q.32
If the electric field is given by , calculate the electric flux through a surface of area 20 units lying in Y – Z plane.
Ans: 120 units
Q.33
The electric field in a certain region of space is ´105 N/C. Calculate electric flux due to this field over an area of ´10-2 m2.
Ans: 6×103 NC-1 m2
Q.34
Careful measurement of the electric field at the surface of a black box indicates that the net outward flux through the surface of the box is 8.0×103 NC-1 m2. (a) What is the net charge inside the box? (b) If the net outward flux through the surface of the box were zero, could you conclude that there were no charges inside the box? Why or why not?
Ans: 0.07 mC; No; any number of charges may be present inside but algebraic sum of these charges in zero.
Q.35
A point charges cause an electric flux of – 1.0´x103 Nm2/C to pass through a spherical Gaussian surface of 10.0 cm radius centred on the charge. (a) If the radius of the Gaussian surface were doubled, how much flux would pass through the surface? (b) What is the value of the point charge?
Ans: -1.0×103 Nm2 C-1 ; -8.85×10-9 C
Q.36
A spherical conductor of radius 12 cm has a charge of 1.6×10-7 C distributed uniformly on its surface. What is the electric field (a) inside the sphere (b) just outside the sphere (c) at a point 18 cm. from the centre of the sphere ?
Ans: (a) Zero (b) 105 NC-1 (c) 4.4×104 NC-1
Q.37
Two large, thin metal plates are parallel and close to each other. On their inner faces, the plates have surface charge densities of opposite signs and of magnitude 17.0×10-12 Cm-2. What is E (a) to the left of the plates (b) to the right of the plates (c) in between the plates?
Ans: (a) Zero (b) Zero (c) 1.9 N/C
Q.38
A particle of mass 5×10-6 g is kept over a large horizontal sheet of charge density 4×10-6 C/m2. What charge should be given to this particle, so that if released, it does not fall down. How many electrons are to be removed to give this charge?
Ans: 2.16×10-13 C; 1.355×106
Q.39
The electric field in a region is radially outward and varies with distance r as E=250 r Vm-2. Calculate the charge contained in a sphere of radius 0.2 m centred at the origin.
Ans: 2.22×10-10 C
Q.40
An electric dipole consists of charges of 2.0×10-8 C separated by a distance of 2 mm. It is placed near a long line charge of density 4.0×10-4 Cm-1 as shown in Fig. Such that the negative charge is at a distance of 2 cm from the line charge. Calculate the force acting on the dipole.
Ans: 0.66 N