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Classical Electroman

The document contains 9 problems related to electrostatics and magnetostatics: 1) Finding the potential, induced surface charge density, and force on a point charge inside a conducting sphere; 2) Finding the electric field in three regions around a spherical shell with a non-uniform charge density; 3) Calculating the work required to assemble a charged sphere; 4) Finding the potential between two coaxial conducting cylinders with opposite uniform line charges; 5) Showing that the force on a current loop in a uniform magnetic field is zero; 6) Deriving the kinetic energy of a particle in a cyclotron; 7) Finding the force on a point charge between two parallel conducting planes; 8) Expanding the potential from line charges

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ayush kumar
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203 views1 page

Classical Electroman

The document contains 9 problems related to electrostatics and magnetostatics: 1) Finding the potential, induced surface charge density, and force on a point charge inside a conducting sphere; 2) Finding the electric field in three regions around a spherical shell with a non-uniform charge density; 3) Calculating the work required to assemble a charged sphere; 4) Finding the potential between two coaxial conducting cylinders with opposite uniform line charges; 5) Showing that the force on a current loop in a uniform magnetic field is zero; 6) Deriving the kinetic energy of a particle in a cyclotron; 7) Finding the force on a point charge between two parallel conducting planes; 8) Expanding the potential from line charges

Uploaded by

ayush kumar
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as PDF, TXT or read online on Scribd
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Instructor: Dr. J.

Mohanty

1. Using the method of images, discuss the problem of a point charge q inside a hollow, grounded,
conducting sphere of inner radius r. Find (a) the potential inside the sphere; (b) the induced surface-
charge density; (c) the magnitude and direction of the force acting on q. (d) Is there any change in
the solution if the sphere is kept at a fixed potential V? If the sphere has a total charge Q on its inner
and outer surfaces?
2. A hollow spherical shell carries charge density ρ = k/r2 in the region a ≤ r ≤ b. Find the electric field
in the three regions: (i)r < a, (ii)a < r < b, (iii)r > b. Plot E as a function of r.
3. Find the work it takes to assemble a sphere of radius R and charge Q by summing over the work to
add a shell of thickness dr on top of a sphere of radius r using any result from the previous problem.
Verify that this equals the volume integral of the field energy density 0 E 2 /2.
4. Consider an infinitely long hollow conducting cylinder of radius a and charge λ per unit length sur-
rounded by an outer hollow conducting cylinder of radius b with charge −λ per unit length. Find
V (r)∀r, where r is the radial distance from the axis.
5. Show that the force on a closed current carrying loop in a uniform magnetic field is zero. Deduce that
the force on a segment of wire of any shape, starting from A and ending at B in a uniform field is the
same as that on a straight wire joining A and B carrying the same current.

6. Show that when the particle in a cyclotron has an orbit of radius R, its kinetic energy is K =
q 2 B 2 R2 /2m. If a cyclotron is to accelerate protons to a kinetic energy K = 4M eV what must be
its radius if the field is B = 4T ?
7. Two infinite parallel grounded conducting planes are held a distance a apart. A point charge q is
placed in the region between them, a distance x from one plate. Find the force on q. Check that your
answer is correct for the special cases (i)a −→ ∞, (ii)x = a/2.
8. A thin insulating rod, running from z = −a to z = +a, carries the indicated line charges. In each
case, find the leading term in the multipole expansion of the potential: (a)λ = kcos(πz/2a), (b)λ =
ksin(πz/a), (c)λ = kcos(πz/2a), where k is a constant.

9. The electric potential of some configuration is given by the expression V (r) = A(e−λr /r), where A and
λ are constants. Find the electric field E(r), the charge density ρ(r), and the total charge Q.

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