CHAPTER CONTAIN: ELECTROSTATIC FIELD AND POTENTIAL, CAPACITOR
THIS TEST CONTAINS 50 NUMBER OF QUESTIONS WITH SINGLE OPTION CORRECT. EACH QUESTION CARRY 4 MARKS AND TIME DURATION OF THIS TEST IS 1 HOUR 50 MINUTES.
ELECTROSTATICS TEST 1 contains 50 number of mcq with single option correct. Each question carry 4 marks. Total marks of the test is 200 and time is 1 hour 30 minutes.
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Suppose the charge of a proton and an electron differ slightly. One of them is –e, the other is (e + ∆e). If the net of the electrostatic force and gravitational force between two hydrogen atoms placed at a distance d (much greater than atomic size) apart is zero, then ∆e is of the order of [Given: mass of hydrogen = 1.67 kg]
A. C
B. C
C. C
D. C
Two identical charged spheres suspended from a common point by two massless strings of lengths l, are initially at a distance d (d l) apart because of their mutual repulsion. The charges begin to leak from both the spheres at a constant rate. As a result, the spheres approach each other with a velocity v. Then v varies as a function of the distance x between the spheres, as
A.
B.
C.
D.
A charge q is placed at the centre of the line joining two equal charges Q. The system of the three charges will be in equilibrium if q is equal to
A. –
B.
C. –
D.
Four point charges –Q, q, 2q and 2Q are placed, one at each corner of the square. The relation between Q and q for which the potential at the centre of the square is zero is
A. Q = q
B. Q = –
C. Q = q
D. Q =
Three charges —q_{1}, +q_{2} and q_{3} are place as shown in the figure. The x – component of the force on – q_{1} is proportional to
A. –
B. +
C.
D.
Two spherical conductors B and C having equal radii and carrying equal charges on them repel each other with a force F when kept apart at some distance. A third spherical conductor A having same radius as that B but uncharged is brought in contact with B, then brought in contact with C and finally removed away from both. The new force of repulsion between B and C is
A.
B.
C.
D.
A charged oil drop is suspended in a uniform field of 3^{ }Vm^{ 1} so that it neither falls nor rises. The charge on the drop will be (Take the mass of the charge = 9.9 10^{—15} kg and g = 10ms^{2})
A. 1.6 10 ^{18} C
B. 3.2 10 ^{18} C
C. 3.3 10 ^{18} C
D. 4.8 10 ^{18} C
Three point charges +q, 2q and +q are placed at points (x = 0, y = a, z = 0), (x = 0, y = 0, z = 0) and (x = a, y = 0, z = 0) respectively. The magnitude and direction of the electric dipole moment vector of this charge assembly are
A. qa along the line joining points (x = 0, y = 0, z = 0), and (x = a, y = a, z = 0)
B. qa along the line joining points (x=0, y=0, z=0), and (x=a, y=a, z=0)
C. qa along + x direction
D. qa along + y direction
The electric field in a certain region is acting radially outward and is given by E = Ar where A is a constant. A charge contained in a sphere of radius ‘a’ centred at the origin of the field, will be given by
A.
B.
C.
D.
What is the flux through a cube of side a if a point charge of q is at one of its corner?
A.
B.
C.
D.
A square surface of side L meter in the plane of the paper is placed in a uniform electric field E (Vm^{ 1}) acting along the same plane at an angle θ with the horizontal side of the square as shown in the figure. The electric flux linked to the surface, in units of Vm is
A.
B.
C.
D. zero
If the electric flux entering and leaving an enclosed surface respectively is φ_{1} and φ_{2}, the electric charge inside the surface will be
A.
B.
C.
D.
A thin conducting ring of radius R is given a charge +Q. The electric field at the centre O of the ring due to the charge on the part AKB of the ring is E. The electric field at the centre due to the charge on the part ADCB of the ring is
A. E along KO
B. 3E along OK
C. 3E along KO
D. E along OK
Two point charges + 8q and – 2q are located at x = 0 and x = L. A point on the x axis at which the net electric ﬁeld due to these two point charges is zero is
A.
B. 2L
C. 4L
D. 8L
The region between two concentric spheres of radius ‘a’ and ‘b’, respectively (b a) have volume charge density ρ = , where A is a constant and r is the distance from the centre. At the centre of the sphere, there is a point charge Q . The value of A such that the electric field in the region between the spheres will be constant is
The diagrams below show regions of equipotentials.
A positive charged is moved from A to B in each diagram.
A. In all the four cases the work done is the same.
B. Minimum work is required to move q in the figure (I)
C. Maximum work is required to move q in the figure (II)
D. Maximum work is required to move q in figure (III)
–q are placed at points A and B respectively which are at a distance 2L apart, C is the mid point between A and B. The work done in moving a charge +Q along the semi circle CRD is
An electric dipole is placed at an angle of 30^{0} with electric field intensity 2 10^{5} NC ^{1}. It experiences a torque equal to 4 Nm. The charge on the dipole, if the dipole length is 2 cm, is
A. 8 mC
B. 2 mC
C. 5 mC
D. 7 mC
The electric potential V at any point (x, y, z) all in meters in space is given by V = 4x^{2} volt. The electric field at the point (1, 0, 2) in Vm^{ 1}, is
A. 8 along negative X axis
B. 8 along positive X axis
C. 16 along negative X axis
D. 16 along positive X axis
The potential at a point x (measured in µm) due to some charges situated on the xaxis is given by V(x) = volt. The electric ﬁeld E at
x = 4 µm is given by
and in the +ve x direction
and in the – ve x direction
and in the +ve x direction
and in the – ve x direction
A, B and C are three points in a uniform electric field. The electric potential is
A. maximum at C
B. same at all the three points A, B and C
C. maximum at A
D. maximum at B
Assume that an electric ﬁeld = 30x^{2}î exists in space. Then the potential difference V_{A} – Vo, where Vo is the potential at the origin and V_{A} the potential at x = 2 m is
A. 120V
B. 120V
C. 80V
D. 80V
A thin spherical conducting shell of radius R has a charge q. Another charge Q is placed at the centre of the shell. The electrostatic potential at a point P a distance from the centre of the shell is
A bullet of mass 2 g is having a charge of 2 µC. Through what potential difference must it be accelerated, starting from rest, to acquire a speed of
10 ms^{ 1 }?
A. 5 kV
B. 50 kV
C. 5 V
D. 50 V
A particle of mass m and charge q is placed at rest in a uniform electric field E then released. The kinetic energy attained by the particle after moving a distance y is
A. qEy
A charge particle q is shot towards another charge particle Q which is fixed, with a speed v. It approaches Q upto a closest distance r and then returns. If q were given a speed of 2v, the closest distance of approach would be
B. 2r
C. r
Two thin wire rings each having a radius R are placed at a distance d apart with their axes coinciding. The charges on the two rings are +q and q. The potential difference between the centres of the two rings is
The electrostatic potential inside a charged spherical ball is given by φ = ar^{2} + b where r is the distance from the centre and a, b are constants. Then the volume charge density inside the ball is:
A uniformly charged solid sphere of radius R has potential V_{0} (measured with respect to ) on its surface. For this sphere the equipotential surfaces with potentials , , and have radius R_{1}, R_{2}, R_{3} and R_{4} respectively. Then
A capacitor of 2 µF is charged as shown in the diagram. When the switch is turned to position 2, the percentage of its stored energy dissipated is of 2 µF is charged as shown in the diagram. When the switch is turned to position 2, the percentage of its stored energy dissipated is
A. 75%
B. 80%
C. 0%
D. 20%
Two condensers, one of capacity C and other of capacity are connected to a Vvolt battery, as shown in the figure. The work done in charging fully both the condensers is
What is the effective capacitance between points X and Y?
A combination of capacitors is set up as shown in the figure. The magnitude of the electric field, due to a point charge Q (having a charge equal to the sum of the charges on the 4 µF and 9 µF capacitors), at a point distance 30 m from it, would equal
A parallel plate air capacitor of capacitance C is connected to a cell of emf V and then disconnected from it. A dielectric slab of dielectric constant K, which can just fill the air gap of the capacitor, is now inserted in it. Which of the following is incorrect?
A. The change in energy stored is
B. The charge on the capacitor is not conserved.
C. The potential difference between the plates decreases K times.
D. The energy stored in the capacitor decreases K times.
Two metallic spheres of radii 1 cm and 3 cm are given charges of 1 10 ^{2 }C and 5 10 ^{2 }C, respectively. If these are connected by a conducting wire, the final charge on the bigger sphere is
In the given circuit, charge Q_{2} on the 2µF capacitor changes as C is varied from 1 µF to 3 µF. Q_{2} as a function of ‘C’ is given properly by: (figure are drawn schematically and are not to scale)
A fully charged capacitor has a capacitance ‘C’. It is discharged through a small coil of resistance wire embedded in a thermally insulated block of specific heat capacity ‘S’ and mass ‘m’. If the temperature of the block is raised by ‘ T ’, the potential difference ‘ V’ across the capacitance is
Two spherical conductors A and B of radii 1 mm and 2 mm are separated by a distance of 5 cm and are uniformly charged. If the spheres are connected by a conducting wire then in equilibrium condition, the ratio of the magnitude of the electric ﬁelds at the surfaces of spheres A and B is
A. 4:1
B. 1:2
C 2:1
D. 1:4
This question contains Statement1 and Statement2. Of the four choices given after the statements, choose the one that best describes the two statements.
Statement1 : For a charged particle moving from point P to point Q, the net work done by an electrostatic ﬁeld on the particle is independent of the path connecting point P to point Q.
Statement2 : The net work done by a conservative force on an object moving along a closed loop is zero.
A. Statement 1 is true, Statement 2 is true; Statement2 is the correct explanation of Statement – 1
B. Statement 1 is true, Statement2 is true; Statement2 is not the correct explanation of Statement1
C. Statement1 is false, Statement2 is true.
D. Statement1 is true, Statement2 is false.
A Parallel plate capacitor is made of two circular plates separated by a distance 5 mm and with a dielectric of dielectric constant 2.2 between them. When the electric field in the dielectric is 3 x 10^{4 }Vm^{ 1}, the charge density of the positive plate will be close to:
A. 6 10^{7 }Cm^{2}
B. 3 10^{7 }Cm ^{2}
C. 3 10^{4 }Cm ^{2}
D. 6 10^{4 }Cm ^{2}
A simple pendulum has a length l and the mass of the bob is m. The bob is given a charge q coulomb. The pendulum is suspended between the vertical plates of a charged parallel plate capacitor. If E is the electric field strength between the plates, the time period of the pendulum is given by
Two identical metal spheres charged with + 12 µC and – 8 µC are kept at certain distance in air. They are brought into contact and then kept at the same distance. The ratio of the magnitudes of electrostatic forces between them before and after contact is
A. 12:1
B. 8:1
C. 24:1
D. 4:1
When a soap babble is given an electric charge
A. it contracts
B. it expands
C. its size remain the same
D. it expands or it contracts depending upon whatever the charge is positive or negative
Two identical conducting balls A and B have positive charges q_{1} and q_{2} respectively. But q_{1} q_{2}. The balls are brought together so that they touch each other and then kept in their original positions. The force between them is
A. less than that before the balls touched
B. greater than that before the balls touched
C. same as that before the balls touched
D. zero
If q_{1} + q_{2} = q, then the value of the ratio , for which the force between q_{1} and q_{2} is maximum is
A. 0.25
B. 0.75
C. 1
D. 0.5
Two equal point charges each of 3 µC are separated by a certain distance in metres. If they are located at (î +ĵ +k̂) and (2î +3ĵ +3k̂), then the electrostatic force between them is
A. 9 10^{3} N
B. 9 10^{3} N
C. 10^{3} N
D. 9 10^{2} N
A charge Q is distributed uniformly in a sphere (solid). Then the electric field intensity any point r, where r < R (R is the radius of sphere) varies as
A.
B.
C. r
D.
A body in the form of a right circular cone of dielectric material with base radius R and height h is placed with its base on a horizontal table. A horizontal uniform electric field of magnitude E penetrates the cone. The electric flux that enters the body is
A.
B. ERh
C.
D. 2ERh
The charge given to any conductor resides on its outer surface, because
A. the free charge tends to be in its minimum potential energy state.
B. the free charge tends to be in its minimum kinetic energy state.
C. the free charge tends to be in its maximum potential energy state.
D. the free charge tends to be in its maximum kinetic energy state.
Three charges q, 2q and 2q are placed at the vertices of an equilateral triangle of side a. The work done by some external force to increase their separation to 2a will be
A. negative
B.
C.
D. zero