A hollow cylindrical box of length 1m and area of cross-section 25 cm2 is placed in a three dimensional coordinate system as shown in the figure. The electric field in the region is given by E→=50xi^ where E is in NC-1 and x is in metres. Find
Answer:
A charge ‘q’ is placed at the centre of a cube of side l. What is the electric flux passing through each face of the cube? (All India 2012)
Using Gauss’ law deduce the expression for the electric field due to a uniformly charged spherical conducting shell of radius R at a point
(i) outside and
(ii) inside the shell.
Plot a graph showing variation of electric field as a function of r > R and r < R (r being the distance from the centre of the shell) (All India)
What is the electric flux through a cube of side 1 cm which encloses an electric dipole? (Delhi 2015)
Why must electrostatic field be normal to the surface at every point of a charged conductor? (Delhi 2012)
How does the electric flux due to a point charge enclosed by a spherical Gaussian surface get affected when its radius is increased? (Delhi 2016)
Does the charge given to a metallic sphere depend on whether it is hollow or solid? Give reason for your answer. (Delhi 2017)
Why are electric field lines perpendicular at a point on an equipotential surface of a conductor? (Comptt. All India 2015)
Name the physical quantity whose S.I. unit is JC-1. Is it a scalar or a vector quantity? (All India 2010)
A sphere S1 of radius r1 encloses a net charge Q. If there is another concentric sphere S2 of radius r2 (r2 > r,) enclosing charge 2Q, find the ratio of the electric flux through S1 and S2. How will the electric flux through sphere S1 change if a medium of dielectric constant K is introduced in the space inside S2 in place of air? (Comptt. All India 2014)
Show on a plot the nature of variation of the
distance ‘d’ apart as shown in the figure. The electric field intensity is zero at a point ’P’ on the line joining them as shown. Write two conclusions that you can draw from this. (Comptt. Delhi 2014)
Given a uniform electric field E→ = 2 × 103 i^ N/ C, find the flux of this field through a square of side 20 cm, whose plane is parallel to the y-z plane. What would be the flux through the same square, if the plane makes an angle of 30° with the x-axis? (Delhi 2014)
Two charges of magnitudes – 2Q and + Q are located at points (a, 0) and (4a,0) respectively. What is the electric flux due to these charges through a sphere of radius ‘3a’ with its centre at the origin? (All India 2013)
Two charges of magnitudes -3Q and + 2Q are located at points (a, 0) and (4a, 0) respectively. What is the electric flux due to these charges through a sphere of radius ‘5a’ with its centre at the origin?
Define electric flux. Write its S.I. unit.
A charge q is enclosed by a spherical surface of radius R. If the radius is reduced to half, how would the electric flux through the surface change? (All India 2009)
A charge ‘q’ is placed at the centre of a cube of side l. What is the electric flux passing through two opposite faces of the cube? (All India)
Depict the direction of the magnetic field lines due to a circular current carrying loop. (Comptt. Delhi 2012)
Which orientation of an electric dipole in a uniform electric field would correspond to stable equilibrium ? (All India 2008)
A point charge +Q is placed in the vicinity of a conducting surface. Draw the electric field lines between the surface and the charge.
(Comptt. Outside Delhi 2017)
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?
State Gauss’s law.
A thin straight infinitely long conducting wire of linear charge density ‘X’ is enclosed by a cy¬lindrical surface of radius V and length ‘l’—its axis coinciding with the length of the wire. Obtain the expression for the electric field, indi¬cating its direction, at a point on the surface of the cylinder. (Comptt. Delhi 2012)
Five charges q1, q2, q3, q4 and q5 are fixed at their positions as shown in
figure, S is a Gaussian surface. The Gauss' law is given by
Which of the following statements is correct?
(a) E on the LHS of the above equation will have a contribution from q1 ,q5 and q1, q5 and q3 while q on the RHS will have a contribution from q1 and q4 only
(b) E on the LHS of the above equation will have a contribution from all charges while q on the RHS will have a contribution from q2 and q4 only
(c) E on the LHS of the above equation will have a contribution from all charges while q on the RHS will have a contribution from q1, q3 and q5 only
(d) Both E on the LHS and q on the RHS will have contributions from q2 and q4 only
If the radius of the Gaussian surface enclosing a charge is halved, how does the electric flux through the Gaussian surface change ?
A hemisphere is uniformly charged positively. The electric field at a point on a diameter away from the centre is directed .
(a) perpendicular to the diameter
(b) parallel to the diameter
(c) at an angle tilted towards the diameter
(d) at an angle tilted away from the diameter
In which orientation, a dipole placed in a uniform electric field is in
(i) Use Gauss’s law to find the electric field due to a uniformly charged infinite plane sheet. What is the direction of field for positive and negative charge densities?
(ii) Find the ratio of the potential differences that must be applied across the parallel and series combination of two capacitors Cj and C2 with their capacitances in the ratio 1 : 2 so that the energy stored in the two cases becomes the same. (All India 2016)
Write the expression for the work done on an electric dipole of dipole moment p in turning it from its position of stable equilibrium to a position of unstable equilibrium in a uniform electric
field E. (Comptt. Delhi 2013)
Plot a graph showing the variation of coulomb force (F) versus (1r2), where r is the distance between the two charges of each pair of charges : (1µC, 2µC) and (2µC, – 3µC). Interpret the graphs obtained. (All India 2010)
Two charged spherical conductors of radii R1 and R2 when connected by a conducting wire acquire charges q1 and q2 respectively. Find the ratio of their surface charge densities in terms of their radii. (Delhi 2014)
Consider a region inside which there are various types of charges but the total charge is zero. At points outside the region,
(a) the electric field is necessarily zero
(b) the electric field is due to the dipole moment of the charge distribution only j
(c) the dominant electric field is ∠1/r3, for large r, where r is the distance from an origin in this regions r
(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 figure and a Gaussian surface of radius R with Q at the centre. Then,
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?
Consider a coin of Question . ft is electrically neutral and contains equal amounts of positive and negative charge of magnitude 34.8 kC. Suppose that these equal charges were concentrated in two point charges separated by
(i) 1 cm — (1/2 x diagonal of the one paisa coin)
(ii) 100 m (~ length of a long building)
(iii) 106 m (radius of the earth). Find the force on each such point charge in each of the three cases. What do you conclude from these results?
Consider a sphere of radius R with charge density distributed as p(r) = kr for r <= R
= 0 for r > R.
(a) Find the electric field at all points r.
(b) Suppose the total charge on the sphere is 2e where e is the electron charge. Where can two protons be embedded such that the force on each of them is zero. Assume that the introduction of the proton does not alter the negative charge distribution?
Figure shows three point charges, +2q, -q and + 3q. Two charges +2q and -q are enclosed within a surface ‘S’. What is the electric flux due to this configuration through the surface ‘S’ (Delhi 2010)
A spherical conducting shell of inner radius rx and outer radius r2 has a charge ‘Q’. A charge ‘q’ is placed at the centre of the shell.
(a) What is the surface charge density on the
(i) inner surface,
(ii) outer surface of the shell?
(b) Write the expression for the electric field at a point x > r2 from the centre of the shell. (All India 2010)
(a) Define electric flux. Write its SI units.
(b) The electric field components due to a charge inside the cube of side 0.1 m are as shown :
Ex = ax, where α = 500 N/C-m
Calculate
(i) the flux through the cube, and
(ii) the charge inside the cube. (All India 2008)
Define electric dipole moment. Is it a scalar or a vector? Derive the expression for the electric field of a dipole at a point on the equatorial
plane of the dipole. (All India 2013)
(a) Derive the expression for the energy stored in a parallel plate capacitor. Hence obtain the expression for the energy density of the electric field.
(b) A fully charged parallel plate capacitor is connected across an uncharged identical capacitor. Show that the energy stored in the combination is less than that stored initially in the single capacitor. (All India 2015)
The electric field at a point is
(a) always continuous
(b) continuous if there is no charge at that point
(c) discontinuous only if there is a negative charge at that point
(d) discontinuous if there is a charge at that point
An arbitrary surface encloses a dipole. What is the electric flux through this surface?
