Electrostatic Fields and Forces are conservative. So Work done in an Electrostatic field is Path independent. And path independent work can be accounted as Energy in conservative fields.

Is an electric field of the type shown by the electric lines physically possible?

Explanation of Electric Potential. Is potential property of field ?

Mark the correct statement : (a) If E is zero at certain point, then V should be zero at that point. (b) If E is not zero at certain point, then V should not be zero at that point. (c) If V is zero at certain point, then E should be zero at that point. (d) If V is zero at certain point, then E may or may not be zero.

The electric field lines are closer at point A than at point B.

We can conclude

a) the potential near A is greater than the potential near B

b) the potential near A is less than the potential near B

c) the potential near A is equal to the potential near B

d) nothing can be said about relative potentials near A and B

Potential is minimum atx (a) A (b) B (c) C (d) D

An electron is released from rest in a region of space with a non-zero electric field. Which of the following statements is true?

a) the electron will begin moving towards a region of higher potential.

b) the electron will begin moving towards a region of lower potential.

c) the electron will begin moving along a line of constant potential.

d) nothing can be concluded unless the direction of the electric field is known.

When a 1 mC of charge is carried from point A to point B, the amount of work done by electric field is 100 mJ. What is the potential difference and which point is at a higher potential ?

a) 100 V, B

b) 100 V, A

c) Both are at same potential

Electric Potential of a Point charge

At a point near a point charge, the values of electric field intensity and potential are 9 NC-1 and 9 JC-1, respectively. Calculate the

a) magnitude of the charge, and

b) distance of the charge from the point.

Calculating the Field from Potential. Discussion on Partial Derivatives.

The electric potential V at any point ( x, y, z ) in space is given by V = 4x2 volt where x, y and z are all in metre. The electric field at the point ( 2 m, 0, 4 m ) in Vm-1 is

a) 16 along negative x-axis

b) 16 along positive x-axis

c) 32 along negative x-axis

d) 32 along positive x-axis

The graph of Ex along the x axis is as shown in the figure.

Find the graph V( x ). Assume V = 10 V at x = 0.

Electric Potential due to a charged Ring

There are two thin rings, each of radius R, whose axes coincide. The charges of rings are Q1 and Q2. Find the work done to take a charge +q from the center of first ring to the center of second ring.

Electric Potential due to a charged Disk

A plastic disk of radius R is charged on one side with a uniform surface charge density s, and then three quadrants of the disk are removed. With V = 0 at infinity, what is the potential due to the remaining quadrant at point P, which is on the central axis of the original disk at distance d from the original center ?

Electric Potential due to a charged Hollow Sphere (Spherical Shell)

A charge Q is distributed over two concentric hollow spheres of radius r and R ( R > r ) such that their surface densities are equal.

Find the charge on shells and potential at the common centre?

Electric Potential due to a charged Solid sphere.

A non-conducting sphere of radius R = 5 cm has its centre at the origin O of coordinate system as shown in fig. Its has two spherical cavities of radius r = 1 cm, whose centres are at ( 0, 3 cm ), ( 0, - 3 cm ), respectively, and solid material of the sphere has uniform positive charge density r = 1/p mCm-3.

Calculate electric potential at point P ( 4 cm, 0 , 0).

Electric Potential due to a Line of Charge ( Finite, Semi-Infinite and Infinite )

A wire having a uniform linear charge density l is bent into the shape as shown.

Find

(a) the electrical field and

(b) the electric potential at point O.

Electric Potential due to a charged Sheet

The figure shows three pairs of parallel plates with the same separation. Potential difference between the plates is given to us.

a) Show the direction of Field in each case

b) Rank the plates according to the magnitude of the electric field.

Electric Potential due to an Electric Dipole

Positive and negative point charges of equal magnitude are kept at ( 0, 0, a / 2 ) and ( 0, 0, - a / 2 ) respectively. The work done by the electric field when another positive point charge is moved from ( - a, 0, 0 ) to ( 0, a, 0 ) is

a) positive

b) negative

c) zero

d) depends on the path connecting the initial and final positions

Two dipoles with dipole moment p are placed as shown. Find the potential at point P.

Electric Potential Energy of a system of charges

Find the work done by external agent in assembling the shown system of charges

Three charges Q, + q and + q are placed at the vertices of a right-angled isosceles triangle as shown in the fig. The net electrostatic energy of the configuration is zero if Q is equal to

Which statement about a system of point charges that are fixed in space is necessarily true? Assuming electrostatic potential energy at infinity to be zero

a) If the electrostatic potential energy of the system is negative, net positive work by an external agent is required to take the charges back to infinity

b) If the electrostatic potential energy of the system is negative, net positive work by an external agent was required to assemble the system of charges

c) If the electrostatic potential energy of the system is zero, all charges in the configuration cannot have same sign

When the separation between two charges is increased, the electric potential energy of the charges

a) increases

b) decreases

c) remain the same

d) may increase or decrease

Electric Potential Energy of an electric Dipole placed in an Electric Field.

For the system shown in fig., find

a) the net force on electric dipole.

b) electrostatic energy of the system.

Consider the two large oppositely charged plates as shown. At which of the marked points shown in the figure would a negatively charged particle have the greatest electrical potential energy?

(a) A

(b) B

(c) C

(d) D

Find the least value of vo for which the particle will cross the origin.

Assume that space is gravity free.

A circular ring of radius R with uniform positive charge density l per unit length is located in the y-z plane with its centre at the origin O. A particle of mass m and positive charge q is projected from the point p ( - 3 R, 0,0 ) on the negative x-axis directly towards O, with initial speed v. Find the smallest (non zero) value of the speed such that the particle does not return to P ?

A particle having charge q and mass m is connected to a string of length L tied to a point O in figure. The particle, string and pivot point all lie on a frictionless horizontal table. The particle is released from rest when the string makes an angle q with a uniform electric field of magnitude E.

Determine the speed of the particle when the string is parallel to the electric field.

A non-conducting disk of radius a and uniform positive surface charge density s is placed on the ground, with its axis vertical. A particle of mass m and positive charge q is dropped, along the axis of the disk, from a height d with zero initial velocity. The particle has q/m = 4eog/s.

a) find the value of d if the particle just reaches the disk

b) find the equilibirum position of particle

c) sketch the potential energy of the particle as a function of its height and find its equilibrium position.

n charged drops, each of radius r and charge q, coalesce to form a big drop of radius R and charge Q. If V is the electric potential and E is the electric field at the surface of a drop then

Two rigid insulated sphere A and B of mass m and 2m, respectively, are given charge Q each and kept on rough horizontal ground as shown in fig. The balls always roll purely. When the ball are released,

a) Mechanical energy of system is conserved

b) Linear momentum of system is conserved

c) Angular momentum of the system is conserved about a point on the ground

d) None of these

A ball of mass 1 kg and charge 1 mC directly projected from infinity toward another ball of mass 2 kg and same charge. The initial velocity of projection is

10 m/s. Find the distance of closest separation and their velocities at the closest separation, if the second ball is

a) fixed

b) free to move

The surface is frictionless.

A ball of mass of 1 kg and charge 10/6 mC is directly projected from infinity towards another fixed ball of charge 5 mC ( as shown ). The initial velocity of projection is 10 m/s. Find the distance and its velocity at the closet separation. Assume that the initial line of motion is at a distance of 1 m from the second fixed charge.

A particle of mass m carrying charge q is projected with velocity v from point P towards an infinite line of charge from a distance 2a. Its speed reduces to zero momentarily at point Q which is at a distance a from the line of charge. if another particle with mass m and charge -q is projected with the same velocity v from P towards the line of charge what will be its speed at Q ?

Three charges each of value q are placed at the corner of an equilatral triangle. A fourth charge Q is placed at the centre of the triangle.

a) Find the net force on charge q.

b) If Q = -q, will the charges at the corners move towards the centre or fly away from it ?

c) For what value of Q will the charges remain stationary ?

d) In situation ( c ), how much work is done in removing the charges to infinity ?

Consider a system of these charges q / 3, q / 3 and -2q / 3 placed at points A, B and C respectively, as shown in the figure. Take O to be the centre of the circle of radius R and angle CAB = 60o

a) The electric field at the point O is

b) The potential energy of the system is zero

c) The magnitude of the force between the charges at C and B is

d) The potential at point O is

Four charges +q, -q, +q and -q are placed in order on the four consecutive corners of a square of side a. Find the work done in interchanging the positions of any two neighbouring charges of opposite sign.

Two small balls having the same mass and charge and located at height h1 and h2 are thrown in the same direction along the horizontal at the same velocity v. The first ball touches the ground at a distance l from the initial vertical.

At what height H2 will the second ball be at this instant?

The air drag and the effect of the charges induced on the ground should be neglected.

A small ball of mass m kg having a charge of q C is suspended by a string of length R m. Another identical ball having the same charge is kept at the point of suspension.

Determine the minimum horizontal velocity which should be imparted to the lower ball so that it can make a complete revolution.

Figure shows a large ceiling having uniform charge density s below which a charge particle of charge q and mass m is hung from point O, through a small string of length R. Calculate the minimum speed of ball at the lowest point

a) for the string to become horizontal

b) for the ball to just complete the circle.

Consider the above cases if the string is replaced with a massless rod.

Two point charges Q1 and Q2 lie along a line at a distance from each other. Figure shows the potential variation along the line of charges. At which of the points 1, 2 and 3 is the electric field zero ? What are signs of the charges Q1 and Q2 and which of the two charges is greater in magnitude ?

Variation of electric potential along x - axis is shown in the figure.

Plot the variation of Electric field along x - axis.

In which region is the magnitude of field greatest.

The electric potential function for an electrical field directed parallel to the x-axis is shown below.

The magnitude of electric field in x-direction in the interval 2 < x < 4 is

a) 2.5 NC-1 b) 5 NC-1 c) -2.5 NC-1 d) -5 NC-1

The intervals in which the magnitude of electric field in x-direction is maximum are

a) -2 ? x ? 0, 4 ? x ? 8 and 0 ? x ? 2

b) -2 ? x ? 0, and 0 ? x ? 2

c) -2 ? x ? 0, 2 ? x ? 4 and 4 ? x ? 8

d) 0 ? x ? 2, and 4 ? x ? 8

The graph Ex versus x will be

Two electric charges q and -2q are placed at a distance a m apart on a horizontal plane. Taking the charge q to be at origin, find the locus of point on this plane where the potential has a value zero.

For this system, there can be

a) Only one point in space where net electric field is zero

b) Only two points in space where net electric potential is zero

c) Infinite number of points in space where net electric field is zero

d) Infinite number of points in space where net electric potential is zero

Two fixed charges - 2Q and Q are located at the points with coordinates ( - 3a, 0 ) and ( + 3a, 0 ), respectively, in the x - y plane.

a) Show that all points in the x - y plane where the electric potential due to the two charges is zero lie on a circle. Find its radius and location of its centre.

b) Give the function of potential V( x ) along x - axis and sketch the function V( x ).

c) If the particle of charge + q starts from rest at the centre of the circle, show that the particle eventually crosses the circle. Find its speed when it does so.

The electric field along x axis is given by A / x3. Then, the potential at a point x, assuming the potential at infinity to be zero, is

a) Zero b) A / 2x2 c) 3A / x4 d) A / x2

A charge +q is fixed at each of the points x = xo, x = 3xo, x = 5xo.... upto infinity and a charge -q is fixed at each of the points x = 2xo, x = 4xo, x = 6xo....upto infinity. Here xo is a positive constant. The potential at the origin to this system of charges is

What is the equation of equipotential lines in x - y plane for a dipole kept at the origin and oriented along x - axis ?

Three identical dipoles with charges q and ?q and separation a between the charges are placed on the corners of an equilateral triangle of side d as shown in figure (a << d). Find the energy of the system.

The potential at any point is given by V = z ( y2 - 4x2 ).

Calculate the expression of the electric field in space.

Small identical balls with equal charges are fixed at the vertices of a symmetric n-sided polygon with side a. At a certain instant one of the balls is released, and after a sufficiently long time, the ball adjacent to the first released ball is released. The kinetic energies of the released balls are found to differ by K at a sufficiently long distance from the polygon.

Determine the charge q of each ball.

Find the electric potential at the point of center of

a) hemisphere

b) slice of a sphere making an angle of q.

Given that the surfaces are a part of sphere with radius R and charged uniformly with the surface density s.

Find the Electrostatic Self Energy (work done to assemble) :

a) a uniformly charged shell with charge Q

b) a uniformly charged sphere with charge Q (volume charge density r)

A thin nonconducting ring of radius R has a linear density l = lo cos q, where lo is a constant. Center of ring is placed at origin in x - y plane.

a) What is the total charge on the ring.

b) What is the potential due to this ring on z axis

b) Find the dipole moment of the ring.

c) Find the magnitude of the electric field and potential at a point on x-axis at

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