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

(c)

Key concept: If the lines of forces are equidistant and parallel straight lines, the field is uniform and if either lines of force are not equidistant, or straight line or both, the field will be non-uniform. The number of electric field lmes passing per unit area is proportional to the strength of electric field. For example, see the following figures:

Hence in given question, from given pattern of electric field lines it is clear that the strength of electric field decreases from left to right. As a result force on charges also decreases from left to right.

Here in given figure, the force on charge -q is greater than force on charge +q in turn dipole will experience a force towards left. Hence option (c) is correct.

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)

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)

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)

Why must electrostatic field be normal to the surface at every point of a charged conductor? (Delhi 2012)

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)

A sphere S_{1} of radius r_{1} encloses a net charge Q. If there is another concentric sphere S_{2} of radius r_{2} (r_{2} > r,) enclosing charge 2Q, find the ratio of the electric flux through S_{1} and S_{2}. How will the electric flux through sphere S_{1} change if a medium of dielectric constant K is introduced in the space inside S_{2} in place of air? (Comptt. All India 2014)

Show on a plot the nature of variation of the

- Electric field (E) and
- potential (V), of a (small) electric dipole with the distance (r) of the field point from the centre of the dipole. (Comptt. Outside Delhi 2016)

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)

Name the physical quantity whose S.I. unit is JC^{-1}. Is it a scalar or a vector quantity? (All India 2010)

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 × 10^{3} 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 -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)

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)

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)

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)

If the radius of the Gaussian surface enclosing a charge is halved, how does the electric flux through the Gaussian surface change ?

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?

Two thin concentric and coplanar spherical shells, of radii a and b (b > a) carry charges, q and Q, respectively. Find the magnitude of the electric field, at a point distant x, from their common centre for

(i) 0 < x < a

(ii) a ≤ x < b

(iii) b ≤ x < ∞ (Comptt. Delhi 2016)

Five charges q_{1}, q_{2}, q_{3}, q_{4} and q_{5} 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 q_{1 },q_{5} and q_{1}, q_{5} and q_{3} while q on the RHS will have a contribution from q_{1} and q_{4} 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 q_{2} and q_{4} 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 q_{1,} q_{3} and q_{5} only

(d) Both E on the LHS and q on the RHS will have contributions from q_{2} and q_{4} only

Two fixed, identical conducting plates (a and P), each of surface area .S' are charged to -Q and q, respectively, where Q > q >0. A third identical plate (j), free to move is located on the other side of the plate with charge q at a distance d (figure). The third plate is released and collides with the plate p. Assume the collision is elastic and the time of collision is sufficient to redistribute charge amongst p and y

(a) Find the electric field acting on the plate y before collision.

(b) Find the charges on P and yafter the collision.

(c) Find the velocity of the plate yafter the collision and at a distance d from the plate /?.

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?

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?

(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 P_{1} and P_{2}.

(c) Draw the pattern of electric field lines in this arrangement. (Comptt. All India 2012)

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

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)

State Gauss’ law in electrostatics. Using this law derive an expression for the electric field due to a uniformly changed infinite plane sheet.

(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)

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 â€” (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?

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

(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 :

E_{x} = ax, where α = 500 N/C^{-m}

Calculate

(i) the flux through the cube, and

(ii) the charge inside the cube. (All India 2008)

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

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.

What is the direction of the electric field at the surface of a charged conductor having charge density σ < 0? (Comptt. Delhi 2012)

State ‘Gauss law’ in electrostatics. Use this law to derive an expression for the electric field due to an infinitely long straight wire of linear charge density λ cm^{-1}

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)