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[NOTES/EM-01006]--Hall Effect

Node id: 5510page

The Hall effect described here provided an early method to study the effect of magnetic field on a current. An expression for Hall voltage and Hall resistance is obtained in this section.

 

 AK-47's picture 22-11-17 18:11:24 n

[NOTES/EM-01002]- Thomson’s Method for e/m

Node id: 5506page

Thomson passed electrons through a region having mutually perpendicular electric and magnetic field, and both perpendicular to the velocity of the electrons. The fields were adjusted so as to produce no deflection. This enebled him to measure the \(e/m\) of electrons. 

 AK-47's picture 22-11-17 18:11:52 n

[SUNDAY-PHYSICS] GATE/JEST/NET Hint for Solutions of Complex Variables Questions

Node id: 5772page
 kapoor's picture 22-11-06 08:11:48 n

Sunday Physics

Node id: 3462forum
 kapoor's picture 22-11-06 06:11:41

[MCQ/CV-02001] Analytic functions

Node id: 5796page

 


Question:

If \(f(z)\)  is an analytic function of \(z\),  \(\left( \frac{\partial^2 }{\partial x^2} + \frac{\partial^2 }{\partial y^2}\right) \left| f(z)\right|^2\) is equal to

(A)  \(2 \big| f^ \prime(z)\big|^2\) (B)  \(3 \big|f^\prime(z)\big|^2\)
(C)  \(4 \big| f^\prime(z)\big|^2\)

(D)  \(8 \big| f^\prime(z)\big|^2\)

 


Hint

Select a simple analytic function and test which option is correct.


Answer

Take \(f(z)=z\) and then it is easy to check  that Option (C) is the correct option.


Full Solution

With choice \(f(z)=z\), we get \( \big|f(z)\big|^2 = (x^2+y^2)\).

Therefore

\(\left( \frac{\partial^2 }{\partial x^2} + \frac{\partial^2 }{\partial y^2}\right) \left| f(z)\right|^2 = 4\)

Also  we have \(f^\prime(z)=1\).

Hence Option (D) is the correct option.


Acknowledgment

Communicated by Sunday-Physics-Participant


 kapoor's picture 22-10-21 15:10:26 n

[PSU/CV-02001] Solution of Equations in Complex Plane --- Solution of Equations

Node id: 5794page
 kapoor's picture 22-10-20 12:10:23 n

[QUIZ/EM-04001] A charge and two infinite planes

Node id: 2992page
 kapoor's picture 22-10-18 11:10:04 n

[QUIZ/EM-04002] A thick spherical shell and a point charge

Node id: 2991page
 kapoor's picture 22-10-18 11:10:30 n

[QUIZ/EM-09001] Electromagnetic Induction

Node id: 3022page

A rod of mass $m$ and length $\ell$ and resistance $R$ rests and is free to slide on two parallel rails of zero resistance as shown in \Figref{em-fig-09008}. A uniform magnetic field fills the area surrounding the rails and is perpendicular and out of the plane of the paper. A battery of of voltage $V$ is connected as shown in the figure.
  1. Qualitatively describe the motion of the rod when the  circuit is  completed by closing the key.
  2. How the motion will change if the connection of the battery polarity is reversed magnetic field remains the same?
  3. How the motion will change if the direction of the magnetic field is reversed and the battery is connected as shown?
kapoor's picture 22-10-18 11:10:54 n

[QUIZ/EM-01001] Equal Point Charges on Corners of a Regular Polygon

Node id: 5792page

 Equal charges \(Q\) are placed on corners of a regular polygon. Show that the electric field at the center of polygon is zero.  Use only geometrical arguments. Do not write any  expressions or equations.
 You may write a small paragraph or draw a figure. \\
 
  The proof is easy for a polygon of even number of sides. How about the case charges on a regular polygon  of odd number of sides?
 Sketch figures to indicate a proof for a regular pentagon.

 kapoor's picture 22-10-18 11:10:17 n

[QUE/TH-01004] TH-PROBLEM

Node id: 5189page
   
   

Express the temperatures given below in $^\circ C,R$, and $^\circ F$. Write your answers in form of table.

  • (a) Triple point of Hydrogen 13.81 K
  • (b) Boiling point of Ne 27.102 K
  • (c) Boiling point of Oxygen 90.188 K
  • (d) Melting point of zinc 692.664
  • (e) Melting point of gold 1337.58

 

SN K C F R
(a)        
(b)        
(c)        
(d)        
(e)        
AK-47's picture 22-10-17 15:10:45 n

SUNDAY-PHYSICS Challenge Problem-02

Node id: 5787page
 kapoor's picture 22-10-17 13:10:27 n

[SUNDAY-PHYSICS/CV-LEC-01] Notes for Session-01 --- When is a Function Analytic ?

Node id: 5608page

NOTES FOR Session-01 Jul 17, 2022

 kapoor's picture 22-10-16 19:10:31 n

Let's Discuss The Postulates :: Consistency of Probability Interpretation

Node id: 4834basic_multi_step
 kapoor's picture 22-10-08 12:10:10 n

Sunday-Physics Challenge Problem-001

Node id: 5783page

Equal charges \(Q\) are placed on corners of a regular polygon. Show that the electric field at the center of polygon is zero.  

This problem is easy to solve by summing over electric field due to individual charges and using trigonometric identities, or something equivalent.
 
The challenge is to find simpler  solution  without writing any  expressions, or equations, without using any complicated identities. Simply  sketch a diagram to indicate a proof for a regular pentagon.

 kapoor's picture 22-10-03 07:10:25 n

SUNDAY-PHYSICS :: Challenge Problems

Node id: 5782collection

Equal charges on a regular polygon

 kapoor's picture 22-10-03 07:10:33 n

SUNDAY PHYSICS --- Lecture 11 , Sept 18, 2022

Node id: 5781page
 kapoor's picture 22-10-03 04:10:34 n

SUNDAY-PHYSICS October 3, 2022 Lecture 12

Node id: 5780page
 kapoor's picture 22-10-03 04:10:30 n

REVQ/EM-03001 Review Questions ---- Sample to Test Ideas

Node id: 5777page

This node has a set of review questions for self test of understanding of  Sec. 3.1 Electric Potential.

 kapoor's picture 22-09-28 05:09:48 n

[AGBX/EM] Anti Gray Boxes --- Electromagnetic Theory

Node id: 5397page
 kapoor's picture 22-09-27 23:09:44 n

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