# Archive for October, 2011

## College of Engineering & Management Kapurthala

2College of Engineering & Management is situated in the district Kapurthala (Punjab) of India.

Affiliated with: Punjab Technical University (PTU), Kapurthala

Approved by: All India Council for Technical Education (AICTE), New Delhi.

**Courses offered:**

B.Tech.

- Computer Science Engineering
- Electronics and Communication Engineering
- Electrical & Electronics Engineering
- Mechanical Engineering
- Information Technology
- Instrumentation & Control Engineering

**Eligibility for Admission in B.Tech. (more…)**

## Chitkara Institute of Engineering & Technology, Patiala

0Chitkara Institute of Engineering & Technology is situated in the district Patiala (Punjab) of India.

**Courses offered:**

B.Tech.

- Computer Science Engineering
- Electronics and Communication Engineering
- Electrical & Electronics Engineering
- Mechanical Engineering

**Eligibility for Admission in B.Tech.**

10+2 Non-Medical (PCM) passed.** **

Administrative Office:

Saraswati Kendra,

SCO 160-161, Sector 9 C, Chandigarh 160 009, India.

Telephone:01724090900, 9501999555

For Admission Queries: 9501105714, 9501105715

For Admission Queries mail to: admissions@chitkara.edu.in

**Address** : Chitkara Institute of Engineering & Technology, Patiala

Address : Chandigarh-Patiala, National Highway, Vill. Jansla,

Mobile No. : 9876894944,

Tel. No. : 01762507084

Tehsil : Rajpura

District : Patiala

Pincode : 140401

Website : http://www.chitkara.edu.in/ciet/

## Chandigarh engineering college Landran, Mohali

0Chandigarh engineering college is situated in the tehsil Landran, city Mohali (Punjab) of India.

Affiliated with: Punjab Technical University (PTU), Kapurthala

Approved by: All India Council for Technical Education (AICTE), New Delhi.

**Courses offered:**

B.Tech.

- Computer Science Engineering
- Electronics and Communication Engineering
- Information Technology
- Mechanical Engineering

**Eligibility for Admission in B.Tech.**

10+2 Non-Medical (PCM) passed.** **

**Admission Procedure**: – (more…)

## Cambridge Engineering College Fatehgarh Sahib

0Cambridge Engineering College is situated in the city Fatehgarh Sahib (Punjab) of India.

Affiliated with: Punjab Technical University (PTU), Kapurthala

Approved by: All India Council for Technical Education (AICTE), New Delhi.

**Courses offered:**

B.Tech.

- Computer Science Engineering
- Civil Engineering
- Electronics and Communication Engineering
- Information Technology
- Mechanical Engineering

**Eligibility for Admission in B.Tech.**

10+2 Non-Medical (PCM) passed.** **

**Admission Procedure**: –

Total seats are classified in 2 categories. Institute can fill 33% of the seats (Management Quota) directly provided the students possess requisite qualification. Balance (67%) seats are filled through counselling conducted by PTU on the basis of ranking in All India Engineering Entrance Exam (AIEEE).

Website: http://www.cambridge.edu.in/

Email : info@cambridge.edu.in

**Address** : **Cambridge**** Engineering College**

Vill. Isherhail, Chandigarh-Fatehgarh Sahib Highway

Fatehgarh Sahib, Punjab, 140406

Phone No.-+91 1763 264001-004

Fax-+91 1763 264005

## London equations: explanation of flux penetration

1As we have already derived the London equations in last article. Now let us

**explain the flux penetration (Meissner effect) from London equations:**

To explain Meissner effect from London equations consider the differential form of Ampere’s circuital law:

del x B = µ_{o}J_{s}

where B is magnetic flux density and J_{s} is current density

Take curl on both sides of above equation

del x (del x B) = µ_{o }(del x J_{s}) (5)

As del x (del x B)= del(del.B) – del^{2}B

Put above equation and London second equation (equation 4 is derived in last article) in equation (5), we get

del(del.B) – del^{2}B = -[( µ_{o} n_{s}e^{2}(B)/m]

But del.B = 0 (Maxwell’s second equation or Gauss law for magnetism)

Therefore above equation becomes

del^{2}B = [( µ_{o} n_{s}e^{2}(B)/m] (6)

del^{2}B = B/λ_{l}^{2 }(7)

where λ_{l}^{2} = m/ µ_{o} n_{s}e^{2}

or λ_{l} = (m/ µ_{o} n_{s}e^{2})^{1/2}

where λ_{l} is known as London’s penetration depth and it has units of length.

The solution of differential equation (7) is

B = B(0)e^{-x/ λ}_{l} (8)

Where B(0) is the field at the surface and x is the depth inside the superconductor. (more…)

## London equations in superconductors: derivation and discussion

3**London Equations:**

As discussed in the Meissner effect that one of the conditions of the superconducting state is that Magnetic flux density (B) = 0 inside the superconductors that is the magnetic flux cannot penetrate inside the superconductor. But experimentally it is not so. The magnetic flux does not suddenly drop to zero inside the surface. The phenomenon of flux penetration inside the superconductors was explained by H. London and F. London.

**Derivation of London first equation:**

Let n_{s} and v_{s} be the number density (number/volume) and velocity of superconducting electrons respectively. The equation of motion or acceleration of electrons in the superconducting state is given by

m(dv_{s}/dt) = -eE

or dv_{s}/dt = -eE/m (1)

where m is the mass of electrons and e is the charge on the electrons.

Also the current density is given by

J_{s} = -n_{s}ev_{s}

Differentiate it with respect to time,

dJ_{s}/dt = -n_{s}e(dv_{s}/dt)

Put equation (1) in above equation, we get

dJ_{s}/dt = (n_{s}e^{2} E)/m (2)

Equation (2) is known as London’s first equation

**Derivation of London second equation: (more…)**

## Type I and Type II superconductors

5Depending upon their behavior in an external magnetic field, superconductors are divided into two types:

a) Type I superconductors and b) Type II superconductors

Let us discuss them one by one:

1) **Type I superconductors**:

a). Type I superconductors are those superconductors which loose their superconductivity very easily or abruptly when placed in the external magnetic field. As you can see from the graph of intensity of magnetization (M) versus applied magnetic field (H), when the Type I superconductor is placed in the magnetic field, it suddenly or easily looses its superconductivity at critical magnetic field (Hc) (point A).

After Hc, the Type I superconductor will become conductor.

b). Type I superconductors are also known as **soft superconductors** because of this reason that is they loose their superconductivity easily.

c) Type I superconductors perfectly obey Meissner effect.

d) Example of Type I superconductors: Aluminum (Hc = 0.0105 Tesla), Zinc (Hc = 0.0054)

2) **Type II superconductors**: (more…)

## Superconductors, critical temperature, critical magnetic field and Meissner effect

4**Superconductors:**

Superconductors are the materials whose conductivity tends to infinite as resistivity tends to zero at critical temperature (transition temperature).

**Critical temperature (T _{c})**: The temperature at which a conductor becomes a superconductor is known as critical temperature.

**Critical Magnetic Field (Hc)**: The magnetic field required to convert the superconductor into a conductor is known as critical magnetic field.

**Critical magnetic field is related with critical temperature as:**

H_{c}(T) = H_{c}(0)[1 – T^{2}/T_{c}^{2}]

**Meissner Effect:**

Suppose there is a conductor placed in a magnetic field at temperature T (refer figure). Then the temperature is decreased till the critical temperature. See what happened (figure). Lines of force are expelled from the superconductor. This is called Meissner effect.

B is not 0 at T > Tc B=0 at T < Tc

**Definition Meissner Effect:** The expulsion of magnetic lines of force from a superconducting specimen when it is cooled below the critical temperature is called Meissner effect.

**To prove that superconductors are diamagnetic by nature:**

B is not 0 at T > Tc B=0 at T < Tc

As B = µ_{0} (H +M)

Where B is magnetic induction or magnetic flux density,

H is applied magnetic field or magnetic field intensity

And M is intensity of magnetization.

For superconductors B = 0

Thus either µ_{0} = 0 or H + M = 0

But µ_{0 }can not be zero,

Thus H + M =0

Or M = -H (1)

By definition of magnetic susceptibility

X = M/H

Put equation (1)

Thus X = -1

But magnetic susceptibility is negative for diamagnetic materials, thus it **proves that superconductors are diamagnetic by nature.**

**Note: This article is referred from my authored book “Electrical Engineering Materials” having ISBN 8127234044.
**

## Bhutta College of Engineering and Technology Ludhiana

0Bhutta College of Engineering and Technology is situated in the city Ludhiana “Manchester of India” (Punjab) of India.

Affiliated with: Punjab Technical University (PTU), Kapurthala

Approved by: All India Council for Technical Education (AICTE), New Delhi.

**Courses offered:**

B.Tech.

- Computer Science Engineering
- Electrical Engineering
- Electronics and Communication Engineering
- Information Technology
- Mechanical Engineering

MBA

**Eligibility for Admission in B.Tech.**

10+2 Non-Medical (PCM) passed.** **

**Admission Procedure**: –

Total seats are classified in 2 categories. Institute can fill 33% of the seats (Management Quota) directly provided the students possess requisite qualification. Balance (67%) seats are filled through counselling conducted by PTU on the basis of ranking in All India Engineering Entrance Exam (AIEEE).

Website: www.bcetldh.org

Email : principalmmsce@yahoo.co.in

**Address** : Bhutta College of Engineering and Technology ,

Ludhiana-Rara Sahib Road, Bhutta, Ludhiana : 141206

Phone No : 98147-98555, 98147-99666, 98147-11888, 98555-53330, 99157-54105

## No signal can travel faster than the speed of the light

0Proof that no signal can travel faster than the speed of the light.

**Solution**: **Method 1**

As relativistic addition of velocity relation is already derived and from Addition of velocity relation

u = (u’ + v)/ (1 + u’(v/c^{2}))

Suppose there is a signal which travels equal to the speed of light that is put u’ = c and then try to solve, the answer will be

u = c

If we put u’ = c and v = c then solve, we get

u = c

It proves that no signal can travel faster than the speed of the light.

**Method 2:**

Suppose there is a signal which travels faster than the speed of light, that is

v > c

By relation of length contraction in relativity

l = l’(√1 – v^{2}/c^{2})

if we put v > c, then l become imaginary but length can not be imaginary. Therefore it prove that no signal can travel faster than the speed of the light.