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[QUE/EM-01011] --- EM-PROBLEM

Node id: 5489page

An alpha particle travels in a circular path of radius $0.45$m in a magnetic field with $B=1.2$ w/m$^2$. Calculate (i) its speed (ii) its period of revolution, and (iii) its kinetic energy. Mass of proton particle = \(1.67\times 10^{-27}\)kg \(\approx 4\times M_p= 4\times938.27\) MeV.

Solution :

  • [(i)] the magnetic force \(eBv\) must be equal to the mass times acceleration. Therefore \begin{equation*} Bev = \frac{Mv^2}{R}, \end{equation*} where \(R\) is the radius of the circular orbit. Hence \begin{equation*} v= \frac{eBR}{M} = \frac{2\times1.6 \times10^{-19}\times 1.2 \times 0.45}{4\times 1.67\times 10^{-27}}\approx 2.7 \times10^7 \text{m/s}. \end{equation*}
  • [(ii)] The time period is \begin{equation*} T = \frac{2\pi R}{v} = \frac{2\times3.14\times 0.45}{2.7\times10^7} \approx10^{-7} \text{ s}. \end{equation*}
  • [(iii)] The kinetic energy is given by \begin{eqnarray}\nonumber \text{K.E.} &=& \frac{1}{2} M v^2= \frac{1}{2}\times (4\times 1.67 \times 10^{-27}) \times \big(2.7\times10^7\big)^2 \\\nonumber &=& 3.26\times 7.29 \times 10^{-13} \approx 23.7 \times 10^{-13} \text{J}. \end{eqnarray}
 AK-47's picture 22-06-18 12:06:19 n

[QUE/EM-01012] --- EM-PROBLEM

Node id: 5490page

Find the direction and magnitude of \(\vec{E}\) at the center of a square
with charges at the corners as shown in figure below. Assume that
\(q= 1\times 10^{-8}\)coul, \(a=5\)cm.

 AK-47's picture 22-06-18 12:06:00 n

[QUE/EM-01013] --- EM-PROBLEM

Node id: 5491page

A "dipole" is formed from a rod of length \(2a\) and two charges \(+q\)
and \(-q\). Two such dipoles are oriented as shown in figure at the end,
their centers being separated by a distance \(R\). Calculate the force
exerted on the left dipole and show that, for \(R>>a\), the force is
approximately given by
\[F=\frac{3p^2}{2\pi\epsilon_0R^4}\]
where \(p=2qa\) is the dipole moment.

 AK-47's picture 22-06-18 12:06:26 n

[QUE/EM-01014] --- EM-PROBLEM

Node id: 5492page

Find the direction and magnitude of $\vec{E}$ at the center of a square
with charges at the corners as shown in figure below. Assume that
$ q= 1\times 10^{-8}$coul, $a=5$cm.

 AK-47's picture 22-06-18 12:06:16 n

[QUE/EM-01016] --- EM-PROBLEM

Node id: 5494page

An electron moving with speed of $5.0\times 10^8$cm/sec is shot parallel to an electric field strength of $1.0\times 10^3 $nt/coul arranged so as to retard its motion.

  • How far will the electron travel in the field before coming (momentarily) to rest ?
  • how much time will elapse?
  • If the electric field ends abruptly after $0.8$ cm, what fraction of its initial energy will the electron loose in traversing the field?
 AK-47's picture 22-06-18 12:06:07 n

Mathematical Physics :: Bundled Lessons

Node id: 3760page 		kapoor's picture 22-06-18 10:06:34 n

[QUE/EM-04014] EM-PROBLEM

Node id: 2391page

Prove that the potential \(\phi(0)\) at the center of a charge-free spherical volume \(V\) is the equal to average of \(\phi(r)\) over the surface \(S\) of the sphere. Using 

  1. Green’s reciprocity relation.
  2. Green's identity\[\iiint d^3r (f \nabla^2 g − g\nabla^2 f ) = \iint \hat{n} · (f \nabla g − g\nabla f) dS\]

 

 kapoor's picture 22-06-17 21:06:04 n

[2018QM/QUIZ-03]

Node id: 2140page

Quantum Mechanics (2018)
A Course Given at University of Hyderabad
Assignments, Quiz, Test and Examination Papers

 kapoor's picture 22-06-17 21:06:38 n

[ALL-RESOURCES-ABOUT] Computing Cross Sections and Life times

Node id: 3446path
 kapoor's picture 22-06-17 20:06:24 n

[ALL-RESOURCES-ABOUT] Green Function

Node id: 2725curated_content
  1. Basic Definiton A simple example
  2. Calculating Green Function
    • Using Fourier Transform
    • Free Particle Schrodinger Equation
    • Green Function for Klein Gordon Equation
  3. EigenfunctionExpansion
  4. Separation of Variables; Example from electrodynamics
  5. Uniqueness Theorem; Method of Images
  6. ApplicationsConverting to an integral equationBoundary Value Problemsin EMTheoryRelation to Energy Eigenvalues and Eigenfunctions
  7. AND MORE

IMPORTANT EACH PART IS SELF CONTAINED. YOU CAN START READING ANY PART, and CONTINUE in ANY ORDER

 

 

 

 kapoor's picture 22-06-17 20:06:23 n

[EWY/EM-01002] How are the Electric and Magnetic Fields Created?

Node id: 5479page
 kapoor's picture 22-06-13 11:06:28 n

[QUE/EM-04001] --- EM-PROBLEM

Node id: 2241page

Solve the problem of a point charge and a grounded conducting sphere by
expanding the Coulomb potential of the point charge in spherical harmonics with
respect to the center of the sphere, solving for the potential for each
\(\ell\) and resumming.

 kapoor's picture 22-06-11 23:06:40 n

[QUE/EM-03015] --- EM-PROBLEM

Node id: 2266page

Six charges are placed at positions given below:

  Charge Position   Charge Position
 1 q (L, 0, 0)  4 - q (-2L,0,0)
2 2q (0, 2L, 0)  5 - 2q (0, 0,3L)
3 3q (0,- 2L, 0)  6 - 3q (0,0,L)

Compute the dipole moment of the system.

 

 

 kapoor's picture 22-06-11 23:06:59 n

[QUE/EM-03024] --- EM-PROBLEM

Node id: 2380page

Find the interaction energy of two interpenetrating spheres of uniform charge density \(\rho_1\) and \(\rho_2\). Let the two spheres have equal radii \(a\) and let the separation of their centers be \(d< a\). Show that  your answer gives the value expected for the limiting case s (a) \(d=0\), and \(d=a\).

Panofsky and Philips

 

 kapoor's picture 22-06-11 23:06:06 n

[QUE/EM-03022] --- EM-PROBLEM

Node id: 2240page

The permanent dipole moment of water molecule is given to be \(1.86\times10^{-18}\) esc-cm.  How much work is done on water molecule if electric field is increased from  zero to 100 volts/cm and the permanent dipoe is rotated from \(\theta=0\) to \(\theta=\pi\)? 
(Be careful about units.)

Atlee Jackson

 kapoor's picture 22-06-11 23:06:58 n

[QUE/EM-02016]

Node id: 5441page

Two spheres each of radius $R$ are placed so that they partially overlap. The
charge densities in the overlap region is zero and in the two non overlapping
regions is $+\rho$ and $-\rho$ respectively as shown in figure.
The separation between the centres of the spheres is $D$.
Show that the electric field in the overlap region is constant.

\FigBelow{100,-35}{50}{0}{em-fig-02002}{Overlapping spheres}\\

 AK-47's picture 22-06-11 13:06:48 n

[QUE/EM-02013]

Node id: 5440page

The electric field due to a line segment of length $2a$, and carrying
a uniform line charge $\lambda$, at a distance $d$ above the mid point is given by
$$ E = \frac{1}{4\pi\epsilon_0} \, \frac{2\lambda a}{d \sqrt{d^2 +a^2}}$$
Use this result to find the electric field of a {\bf square lamina}
(side $2s$), carrying uniform surface charge density $\sigma$, at a distance
$z$ above the center of the disk.

 AK-47's picture 22-06-11 13:06:58 n

[QUE/EM-02004]

Node id: 5443page

Show that the electric field at the center of a regular $N$-sided polygon is <br />zero when equal charges are placed at the corners of the polygon.

 AK-47's picture 22-06-11 13:06:06 n

[QUE/EM-02002]

Node id: 5442page

Three equal charges are placed at the corners of an equilateral triangle.
Show that the electric field at the center is zero.

 AK-47's picture 22-06-11 13:06:30 n

22SJC -- Lectures on Quantum Mechanics --- June 1 - June 16

Node id: 5457collection

Resource for Course  on  Quantum  Mechanics
St Joseph College --- June 1- June 16 (2022)

 

Study Material for the Course

 

Problem Solving

 

More Resources

 

 kapoor's picture 22-06-05 16:06:54 n

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