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
(b)
Key concept: According to Gauss' law, the term qenclosed on the right side of the equation Фs E . dS =qenclosed / ϵ0 includes the sum of all charges enclosed by the surface called (Gaussian surface).
In left side equation, the electric field is due to all the charges present both inside as well as outside the Gaussian surface.
Hence in given question, E on 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. Hence option (b) is correct.
What is the electric flux through a cube of side 1 cm which encloses an electric dipole? (Delhi 2015)
Does the charge given to a metallic sphere depend on whether it is hollow or solid? Give reason for your answer. (Delhi 2017)
Name the physical quantity whose S.I. unit is JC-1. Is it a scalar or a vector quantity? (All India 2010)
Why must electrostatic field be normal to the surface at every point of a charged conductor? (Delhi 2012)
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?
If Фs E . dS = 0 over a surface, then
(a) the electric field inside the surface and on it is zero
(b) the electric field inside the surface is necessarily uniform
(c) the number of flux lines entering the surface must be equal to the number of flux lines leaving it
(d) all charges must necessarily be outside the surface
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)
Why are electric field lines perpendicular at a point on an equipotential surface of a conductor? (Comptt. All India 2015)
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)
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)
Show that the electric field at the surface of a charged conductor is given by E→=σε0n^, where σ is the surface charge density and h is a unit vector normal to the surface in the outward direction. (All India 201
(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)
Figure shows electric field lines in which an electric dipole P is placed as shown. Which of the following statements is correct?
(a) The dipole will not experience any force
(b)The dipole will experience a force towards right
(c)The dipole will experience a force towards left
(d)The dipole will experience a force upwards
Show on a plot the nature of variation of the
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?
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)
Figure represents a crystal unit of cesium chloride, CsCl. The cesium atohis, represented by open circles are situated at the comers of a cube of side 0.40 nm, whereas a Cl atom is situated at
the centre of the Cube.
The Cs atoms are deficient in one electron while the Cl atom carries an excess electron.
(i) What is the net electric field on the Cl atom due to eight Cs atoms?
(ii) Suppose that the Cs atom at the comer A is missing. What is the net force now on the Cl atom due to seven remaining Cs atoms?
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)
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)
State Gauss’ law in electrostatics. Using this law derive an expression for the electric field due to a uniformly changed infinite plane sheet.
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
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?
An electric dipole is placed in a uniform electric field E→ with its dipole moment p⃗ parallel to the field. Find
(i) the work done in turning the dipole till its dipole moment points in the direction
opposite to E→ .
(ii) the orientation of the dipole for which the torque acting on it becomes maximum. (Comptt. All India 2014)
Two point charges + 3q and – 4q are placed at the vertices ‘B’ and ‘C’ of an equilateral triangle ABC of side ‘a’ as given in the figure. Obtain the expression for
(i) the magnitude and
(ii) the direction of the resultant electric field at the vertex A due to these two charges. (Comptt. All India 2014)
A point positive charge is brought near an isolated conducting sphere (figure). The electric field is best given by
(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)
An arbitrary surface encloses a dipole. What is the electric flux through this surface?
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 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)
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)
What will be the total flux through the faces of the cube as given in the figure with side of length a if a charge q is placed at
(a) A a comer 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
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) 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)
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
Is the electric field due to a charge configuration with total charge zero, necessarily zero? Justify. (Comptt. All India 2012)
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)
In figure two positive charges q2 and q3 fixed along the y-axis, exert a net electric force in the +x-direction on a charge q1, fixed along the x-axis. If a positive charge Q is added at (x, 0), the force on q1
(a) shall increase along the positive x-axis
(b) shall decrease along the positive x-axis
(c) shall point along the negative x-axis
(d) shall increase but the direction changes because of the intersection of Q with q2 and q3
A paisa coin is made up of Al-Mg alloy and weight 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.
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)
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?
In which orientation, a dipole placed in a uniform electric field is in
What is the direction of the electric field at the surface of a charged conductor having charge density σ < 0? (Comptt. Delhi 2012)
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)
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)
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)
