Why are electric field lines perpendicular at a point on an equipotential surface of a conductor? (Comptt. All India 2015)
If the electric field lines were not normal to the equipotential surface, it would have a non-zero component along the surface. To move a unit test charge against the direction of the component of the field, work would have to be done which means this surface cannot be equipotential surface.
Hence, electric field lines are perpendicular at a point on an equipotential surface of a conductor.
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)
What is the electric flux through a cube of side 1 cm which encloses an electric dipole? (Delhi 2015)
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)
Does the charge given to a metallic sphere depend on whether it is hollow or solid? Give reason for your answer. (Delhi 2017)
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)
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)
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)
Show on a plot the nature of variation of the
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?
Depict the direction of the magnetic field lines due to a circular current carrying loop. (Comptt. Delhi 2012)
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)
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)
(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)
Which orientation of an electric dipole in a uniform electric field would correspond to stable equilibrium ? (All India 2008)
(a) Define electric flux. Write its S.I. unit. “Gauss’s law in electrostatics is true for any closed surface, no matter what its shape or size is”. Justify this statement with the help of a suitable example.
(b) Use Gauss’s law to prove that the electric field inside a uniformly charged spherical shell is zero. (All India)
(a) Electric flux. The electric lines of force passing through that area, when held normally to the lines of force.
If the radius of the Gaussian surface enclosing a charge is halved, how does the electric flux through the Gaussian surface change ?
(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)
Refer to the arrangement of charges in figure and a Gaussian surface of radius R with Q at the centre. Then,
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?
(a) Two spherical conductors of radii Ra and R2 (R2 > R1) are charged. If they are connected by a conducting wire, find out the ratio of the surface charge densities on them.
(b) A steady current flows in a metallic conductor of non-uniform cross-section. Which of these quantities is constant along the conductor : current, current density, electric field, drift speed? (Comptt. Delhi 2015)
A point positive charge is brought near an isolated conducting sphere (figure). The electric field is best given by
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?
Two charges q and -3q are placed fixed on x-axis separated by a distance d. Where should a third charge 2q be placed such that it will not experience any force?
There is another useful system of units, besides the SI/MKS. A system, called the CGS (Centimeter-Gram-Second) system. In this system, Coulomb's law
is given by F = (Q q/r2)r .
A thin straight infinitely long conducting wire having charge density X is enclosed by a cylindrical surface of radius r and length l, its axis coinciding with the length of the wire. Find the expression for the electric flux through the surface of the cylinder. (All India 2011)
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
Draw a plot showing variation of electric field with distance from the centre of a solid conducting sphere of radius R, having a charge of +Q on its surface. (Comptt. Delhi 2017)
Given a uniform electric field E→=4×103i^ N/C. Find the flux of this field through a square of 5 cm on a side whose plane is parallel to the Y-Z plane. What would be the flux through the same square if the plane makes a 30° angle with the x-axis? (Delhi 2014)
A positive point charge (+ q) is kept in the vicinity of an uncharged conducting plate. Sketch electric field lines originating from the point on to the surface of the plate.
Derive the expression for the electric field at the surface of a charged conductor. (All India) Answer: Representation of electric field, (due to a positive charge)
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)
A point charge +q is placed at a distance d from an isolated conducting plane. The field at a point P on the other side of the plane is
(a) directed perpendicular to the plane and away from the plane
(b) directed perpendicular to the plane but towards the plane
(c) directed radially away from the point charge
(d) directed radially towards the point charge
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?
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)
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
Figure shows the electric field lines around three point charges A, B and C.
(i) Which charges are positive?
(ii) Which charge has the largest magnitude? Why?
(iii) In which region or regions of the picture could the electric field be zero? Justify your answer.
(a) Near A (b) Near B
(c) Near C (d) Nowhere
Define the term ‘electric flux’. Write its S.I. units. What is the flux due to electric field E→=3×103i^ N/C through a square of side 10 cm, when it is held normal to if? (Comptt. All India 2015)
(a) Define electric flux. Write its S.I. unit.
(b) A small metal sphere carrying charge +Q is located at the centre of a spherical cavity inside a large uncharged metallic spherical shell as shown in the figure the expressions for the electric field at points P1 and P2.
(c) Draw the pattern of electric field lines in this arrangement. (Comptt. All India 2012)
