What is an induced charge ? Can there be a net electric field inside an uncharged conductor ? Can there be a net electric field inside a cavity in an uncharged conductor ?
A positive point charge is placed near a neutral conducting sphere.
The net charge of the sphere is
a) negative and distributed uniformly over the surface of the sphere
b) negative and distributed non-uniformly over the entire surface of the sphere
c) negative and appears only at the point on the sphere closest to the point
d) zero and the interior becomes positively charged and the surface becomes negatively charged
e) zero and the interior remains charge free and the surface gets non-uniform charge distribution
Find the electric field at the center of the sphere due to the induced charges on the surface of the sphere.
Will there be any force between the charge and sphere?
Can there be a net electric field inside an charged conductor ? Can there be a net electric field inside a cavity in an charged conductor ?
In which of the following cases, there is a definitely a net force on a conducting sphere.
a) Sphere is Neutral and placed in a Uniform field
b) Sphere is Charged and placed in a Uniform field
c) Sphere is Nebrutral and placed in a Non-Uniform field
d) Sphere is Charged and placed in a Non-Uniform field
A charge is placed inside a cavity in a conductor. Can there be a net electric field inside the body of conductor ? Can there be a net electric field inside the cavity ?
Find the electric field at point A, due to
a) point charge Q
b) induced charges on the inner surface of the shell
c) induced charges on the outer surface of the shell
A conducting spherical shell of outer radius R and inner radius r has no net charge on it. At its center there is a point charge q, and at a distance 2R from its center there is a point charge Q.
a) What is the force on the charge q at the center ?
b) Can we find the force on q, if it is not placed at the center ?
b) Can we find the net force on outer charge ?
A positive point charge Q is kept inside a neutral conducting shell as shown in figure. An external uniform electric field E is applied. Then
a) Force on Q due to E is zero
b) Net Force on Q is zero
c) Force on shell due to E is zero
d) Net Force on shell is zero
e) Net Force acting on Q and conducting shell considered as a system is zero
As shown in figure, a charge of Q1 is kept inside the two shells. A charge Q2 is imparted to the inner shell and a charge Q3 is imparted to the outermost shell.
A charge Q is placed inside a conducting neutral shell. Find the function of electric field in every region.
Repeat the above question if the shell is also given a charge q.
Electric Potential inside and on the surface of a conductor.
A point charge Q is placed at a distance d from the centre of the isolated metallic ball of radius R. Determine the potential of the ball.
A charge Q is kept in an uncharged metallic shell as shown in Figure.
a) Find the potential at a point outside the shell at a distance 3R from the center. b) Find the potential due to Q and due to charges induced on inner surface at that point.
c) What is the potential of shell ?
d) Can we find the potential at a general point inside the shell ? At the center of
A charge Q is placed inside a thick conducting shell, as shown in the figure.
Find the potential in each region, if the shell is:
b) has a net charge q
Two thin concentric conducting spherical shells are given some charges.
a) Outer shell will always be at higher potential irrespective of the sign of charges given to the shells
b) Inner shell will always be at higher potential irrespective of the sign of charges given to the shells
c) Cannot conclude
Charge Q is uniformly distributed within a spherical volume of radius R.
Obtain the expression for the energy of system.
If the same charge is given to a spherical conductor of the same radius R, what will be the energy of this system ?
Two charged concentric conducting shells are connected with a wire.
How does the charge transfer takes place ? Why ?
Consider two concentric conducting shells as shown in the figure.
The inner shell has a charge ?Q on it and Outer shell has a charge +2Q on it.
a) What is the charge on each surface ?
b) If a wire is connected between the inner and outer sphere, what is the charges on outer shell ?
What does Earthing a conductor mean ? What is the effect of Earthing on the charge and Potential of a conductor ?
Consider the two concentric conducting shells with radius R1 and R2, as shown in figure. The inner shell carries a charge Q. The outer shell is grounded
a) Potential at A equals zero
b) Potential at B equals zero
c) Potential at C equals zero
Two spherical concentric conducting shells of radius R1 and R2 are kept as shown in Fig. Inner shell is given a charge Q1 and the outer shell is earthed.
a) Find the charge supplied by the Earth
b) Repeat the above question if the outer shell had a charge Q2 on it
c) If the inner shell is earthed instead, find the new charge on inner shell
Electric Field near the surface of a Conductor is perpendicular to the surface at every point. And charge density is higher at points which are more curved.
Equation of Electric Field near the surface of a conductor and its meaning.
There is an ellipsoidal cavity in a conductor. A positive charge q is placed at the center of the cavity. Points A and B are on the surface of cavity. Which of the following statements is true ?
a) Charge density at A = Charge density at B
b) Electric field near A in the cavity = Electric field near B in the cavity. c) Potential at A = Potential at B
d) None of these
A point charge is placed inside a metallic shell as shown in the figure. Draw the electric lines inside and outside the shell ? What if the entire system is placed in an external field ?
Charge Distribution and Electric Field of Conducting Sheets
A large non conducting sheet is replaced by a large conducting sheet carrying the same charge. Electric field near the sheet a) increases b) decreases c) remains the same
Four large charged conducting sheets are kept parellel to each other. Charge given to each sheet is shown in the figure.
a) Find the charge on each face
b) Find the field in every region
Three uncharged conducting large plates are placed parallel to each other in a uniform electric field E which is perpendicular to the plates. Find the induced charge density on each surface of each plate.
Repeat the above question if the last plate has a charge Q.
Explanation and Derivation of Electrostatic Pressure
Two large metal plate of area A each with charge Q and - Q are kept facing each other. Show that they attract each other with a force of Q2/2Aeo
A uniformly charged thin spherical shell of radius R carries uniform surface charge density of s per unit area. It is made of two hemispherical shells held together by pressing them with force F. F is equal to
Three concentric metallic spherical shells of radii R, 2R, 3R are given charges Q1, Q2, Q3, respectively. It is found that the surface charge densities on the outer surfaces of the shells are equal. Then, the ratio of the charges given to the shells, Q1: Q2: Q3, is
a) 1: 1: 1 b) 1: 2: 3 c) 1: 4: 9 d) 1: 3: 5
A long hollow conducting cylinder is kept coaxially inside another long hollow conducting cylinder of larger radius. Both the cylinders are initially electrically neutral. Under what conditions does a potential difference appears between the two cylinders :
A solid conducting sphere having a charge Q is surrounded by an uncharged concentric conducting spherical shell. The potential difference between the surface of the sphere and the outer surface of the shell is V. If the shell is now given a charge of -3Q, the new potential difference between the same two surfaces is
(a) V (b) 2V
(c) 4V (d) -2V
A hollow cylindrical pipe containing a point charge is sealed with two curved metal caps.
Electric field outside the pipe will be
a) Identical to the field of an isolated point charge
b) Zero, because the metal shields the field
c) Nonzero, but dependent on where the charge is within the pipe
d) Nonzero, but independent of where the charge is within the pipe
A particle with an unknown charge is placed at the center of a conducting spherical shell. The electric field outside of the shell is 4k Q /r2, directed toward the center. Charge on the inner surface is - 2Q.
a) What is the net charge on the shell?
b) What is the charge on the particle at the center of the shell?
c) What is the potential on the shell?
Two spherical cavities of radii a and b are hollowed out from the interior of a neutral conducting sphere of radius R. A point charge is placed in each cavity as shown.
a) Find the surface charge density on each surface
b) Find the electric field inside the cavities and outside the conductor.
A thin uniformly charged ring with radius R and charge q is placed near a conducting sphere of radius R, such that centre of sphere C, lies on the axis at a distance d = 3R from the plane of the ring.
a) What is the potential of the sphere.
b) Find the potential at point A due to induced charges.
c) When the sphere is grounded, what is the total charge on it?
A point object with a charge +Q is placed at the center of a conducting shell of inner radius R, outer radius 2R, and a charge of -4Q. A thin-walled conducting shell of radius 3R and a charge of +4Q is concentric with the point object and the first shell. Taking V = 0 at infinity, find all the distances from the center at which electric potential is zero.
Two conducting sphere, A of radius R1 and B of radius R2, are shown in figure. Both are positively charged and isolated and are far from each other. They are connected by a conducting wire. Then
a) Sphere A has larger charge
b) Sphere B has larger charge
c) Both spheres have same charge
d) Both spheres have same potential
e) Both spheres have same surface charge density
Two isolated metal spheres of radii R and 2R are charged such that both have the same surface charge density s. The spheres are located far away from each other. When they are connected by a thin conducting wire, the new surface charge density on the bigger sphere will be
Three conducting spherical shells are as shown in the figure. a) find the electric potential of the three shells. b) if the inner and outer shells are now connected by a wire, what is the final charge on each shell ?
Three thin conducting spherical shells are as shown in the figure.
a) find the electric potential of each shell.
b) if the inner and outer shells are now connected by a wire, what is the final charge on each shell ?
A system of three thin concentric spherical metal shells is as shown in the figure. A charge Q is given to the middle shell. The inner and outer shells are earthed.
a) What is the amount of the electric charge on the earthed spherical shells ?
b) Find the expression of electric field in each region.
Two concentric shells of radii R and ?R are shown in figure. Initially, a charge Q is imparted to the inner shells. Now key K1 is closed and opened. Then key K2 is closed and opened. After n such cycles, find
a) the charge on inner shell.
b) net charge on outer shell
c) the potential difference between the shells
A very large sphere having charge Q uniformly distributed on the surface is compressed uniformly till its radius reduces to R. The work done by electric forces in this process is
If a thin spherical shell of radius R and charge q is kept inside a thick spherical shell of inner radius 2R, outer radius 3R and total charge 2q
a) Find the charge distribution on each surface .
b) Find the self energy of each charge distribution.
c) Find the total electrostatic energy stored in the system.
a) Find the total electrostatic energy of the configuration.
Find the new charge on each surface and the total electrostatic energy of the configuration when,
b) Outer shell is earthed
c) Inner shell is earthed
Also find the energy lost in form of heat in each case.
The shells are conducting and thin.
Two isolated metallic solid spheres of radii R and 2R are charged such that both of them have same charge Q. The spheres are located far away from each other, and connected by a thin conducting wire. Find the heat dissipated in the wire.
A conducting sphere A of radius r is connected to another conducting sphere B of radius R through a wire with a switch. Spheres are located far from each other.
B is initially uncharged and A is given a charge Q. Spheres are connected and then disconnected. A is recharged such that the charge on it again Q. Spheres are again connected and then disconnected. This procedure is repeated n times.
a) Find the charge and electrostatic energy of sphere B after n such cycles
b) what is the limiting value of this charge and energy as n
A vessel containing a molten metal is maintained at a potential of 5 V. Spherical drops of 2 mm diameter fall from the vessel into an isolated thin walled metal sphere of diameter 10 cm. When the sphere is completely filled with metal, calculate its a) electric potential b) electrical energy
Three metal plates are positively charged and laid parallel to each other as shown in figure. The net charge on the left plate is Q1. The net force on middle plate is F. If the right plate was removed, the force acting on the middle plate will be equal to F/2. Find charge on each plate.
Field created by the plate can be considered to be uniform.
Net electric field in space is produced by a uniform external electric field and the field due to a charged metal plate (which can be considered uniform). Net electric field on the left of the plate is E1 and to the right of plate is E2.
If the force exerted on the plate by the external field is F, what is the charge on the plate.
What is the surface charge density on each surface.