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Practice each question, then open the answer or worked solution.
Consider a region inside which there are various types of charges but the total charge is zero. At points outside the region
The correct answers are
c) the dominant electric field is proportional to 1/r3 for large r, where r is the distance from an origin in this region
d) the work done to move a charged particle along a closed path, away from the region, will be zero
Refer to the arrangement of charges in the figure and a Gaussian surface of radius R with Q at the centre. Then
a) total flux through the surface of the sphere is –Q/ε0
b) field on the surface of the sphere is –Q/4πε0R2
c) flux through the surface of the sphere due to 5Q is zero
d) field on the surface of the sphere due to -2Q is the same everywhere
The correct answers are
a) total flux through the surface of the sphere is –Q/ε0
c) flux through the surface of the sphere due to 5Q is zero
A positive charge Q is uniformly distributed along a circular ring of radius R. A small test charge q is placed at the centre of the ring. Then
a) if q > 0 and is displaced away from the centre in the plane of the ring., it will be pushed back towards the centre
b) if q < 0 and is displaced away from the centre in the plane of the ring, it will never return to the centre and will continue moving till it hits the ring
c) if q < 0, it will perform SHM for small displacement along the axis
d) q at the centre of the ring is in an unstable equilibrium within the plane of the ring for q > 0
The correct answers are
a) if q > 0 and is displaced away from the centre in the plane of the ring., it will be pushed back towards the centre
b) if q < 0 and is displaced away from the centre in the plane of the ring, it will never return to the centre and will continue moving till it hits the ring
d) q at the centre of the ring is in an unstable equilibrium within the plane of the ring for q > 0
Very Short AnswersAn arbitrary surface encloses a dipole. What is the electric flux through this surface?
According to Gauss law, for an enclosed surface, the electric flux is given as:
The net charge on the dipole is given as –q and +q whose sum is equal to zero.
A metallic spherical shell has an inner radius R1 and outer radius R2. A charge Q is placed at the centre of the spherical cavity. What will be surface charge density on
a) the inner surface
b) the outer surface
Q is the charge which is kept at the centre of the spherical cavity. –Q is the charge that is induced in the inner surface and –Q on the outer surface.
σ is the surface charge density
a) σ1 is the surface charge density on the inner surface = Charge/Area =
b) σ2 is the surface charge density on the outer surface =
The dimensions of an atom are of the order of an Angstrom. Thus there must be large electric fields between the protons and electrons. Why, then is the electrostatic field inside a conductor zero?
The electrostatic field inside a conductor is zero as the dimensions of the atom are in the order of an Angstrom and the electrostatic field inside the conductor is caused by the presence of the excess charges.
If the total charge enclosed by a surface is zero, does it imply that the electric field everywhere on the surface is zero? Conversely, if the electric field everywhere on a surface is zero, does it imply that net charge inside is zero.
The total charge enclosed by a surface is zero, it doesn’t imply that the electric field everywhere on the surface is zero and the field may be normal to the surface. Also, the conversely it does imply that the electric field everywhere on the surface is zero.
Sketch the electric field lines for a uniformly charged hollow cylinder shown in the figure.
Following are the side view and top view of the electric field lines for a uniformly charged hollow cylinder.
What will be the total flux through the faces of the cube with a side of length a if a charge q is placed at
a) A: a corner of the cube
b) B: mid-point of an edge of the cube
c) C: centre of a face of the cube
d) D: mid-point of B and C
a) When we consider the charged particle to be placed at the centre of the cube whose side is 2a, then the charge is equally distributed among 8 cubes. Therefore, the total flux through the faces of the cube = q/8ε0
b) When the charge is placed at B, the charge is equally distributed among the 4 cubes. Therefore, the total flux through the four faces is given as = q/4ε0
c) When the charge is placed at C, the charge is shared among 2 cubes equally. Therefore, the total flux through these faces is given as = q/2ε0
d) When the charge is placed at D, the charge is distributed among two cubes and therefore, the total flux is given as = q/2ε0
A paisa coin is made up of Al-Mg alloy and weighs 0.75 g. It has a square shape and its diagonal measures 17 mm. It is electrically neutral and contains equal amounts of positive and negative charges. Treating the paisa coins made up of only Al, find the magnitude of an equal number of positive and negative charges. What conclusion do you draw from this magnitude?
1 molar mass M of Al = 6.023 × 1023 atoms
No.of aluminium atoms in one paise coin = N = 6.023 × 1023/26.9815 × 0.75 = 1.76 ×1022
There are 13 protons and 13 electrons on the Al as the charge number is 13
Magnitude of positive and negative charges = 3.48 × 104 C = 34.8 kC