DIP112-Unit V- Notes English

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UNIT-V

Electric Charge: -

A charge is produced when there is either shortage or excess of electrons on an object. Shortage of electron develops +ve and excess of electrons develop –ve charges.

If there are ‘n’ electrons transferred than charge produced is where ‘n’ is an integer, thus charge is quantized.

= 1.6 × 10 (

The two very basic natures of electric charges

 Like charges repel each other.

 Unlike charges attract each other.

Coulomb’s Law:-

Force of interaction between two point charges in vacuum is directly proportional to the product of charges and inversely proportional to the square of distance between them. Hence

F=

∈

where ∈0 is electrical permeability of free space and its magnitude is 8.85×10-12 C2/N-m2.

Electric Field:-

Electric field due to a charge is the space around the test charge in which it experiences a force.It is defined as the force

charge. Hence =

Or S.I. unit=N/C and also V/m Dimension = [MLT

Properties of Electric field lines:

1. Electric field lines are IMAGINARY LINES

2. They begin and end perpendicularly to the charged surface. 3. They start on a positive charge and end on a negative charge.

4. The tangent to an electric field line at any point gives the direction of the ele 5. They never cross each other.

6. The force experienced by the positive test charge is always in the direction of the tangent to the field line.

Electric Flux:-

It is defined as the total number of electric lines of forces crossing

direction. ϕ = . =

where is the angle between electric field ( Dimension=[ML3 T-3 A-1]

Gauss’s Law

:- According to gauss’s law electric flux surface is 1/ times the total charge enclosed by the surface.

∴ =∫E.dA =

Where = permittivity of free space

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Electrostatic

A charge is produced when there is either shortage or excess of . Shortage of electron develops +ve and excess of electrons

there are ‘n’ electrons transferred than charge produced is ⇒ = ±

is an integer, thus charge is quantized.

)

The two very basic natures of electric charges are

is electrical permeability of free space and its magnitude is

Electric field due to a charge is the space around the test charge in It is defined as the force experienced by a unit positive

E=

∈ Or S.I. unit=N/C and also V/m Dimension = [MLT-3 A-1]; Quantity : Vector

Properties of Electric field lines:

Electric field lines have the following properties:

IMAGINARY LINES.

They begin and end perpendicularly to the charged surface. They start on a positive charge and end on a negative charge.

The tangent to an electric field line at any point gives the direction of the electric field at that point. The force experienced by the positive test charge is always in the direction of the tangent to the field

It is defined as the total number of electric lines of forces crossing

=

is the angle between electric field ( ) and area vector ( ) S.I. unit N-m

According to gauss’s law electric flux of electric field through a closed times the total charge enclosed by the surface.

= permittivity of free space

A charge is produced when there is either shortage or excess of . Shortage of electron develops +ve and excess of electrons

properties:

ctric field at that point. The force experienced by the positive test charge is always in the direction of the tangent to the field

It is defined as the total number of electric lines of forces crossing the surface in a

m2/C and also V-m;

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And Q (=q1+q2+q3+q4), Total charge enclosed in terms of algebraic sum

Principle of Superposition:

-

Let

the total force on a particular charge is the vector sum of forces that it experience due to all other charges.

for a system of three charges the force on q F= F13 + F23 = + F= +

Electric Potential:

-

Electric potential at any point in a region of electric field is defined as the work done in carrying a unit positive charge from infinity to that point.

= / S.I unit = J/C or volt ( It is a scalar quantity

Electric potential at a point due to charged particle point A, in the field of charge q placed a point O q0.

F= ×

The work done in displacing q0, a small distance dx. dW= . = cos1800

∴ The total work done, in displacing a distance x

= ∫ =

We know that electric potential is given by

= ⇒

Potential difference:- Electric potential diference between two points in an electric field is defined

as the amount of workdone per unit positive charge in moving it from one point to other against the electrostatic force field.

= and =

∴ =

By defintion = ⇒

Equipotential Surface:

-

Euipotential Surface is a surface on which the

potential have the same value at all points. In the other words the potential difference between any two points on a equipotential nsurface is zero ( =0).

Electric field lines are always perpendicular to an

equipotential surface.

), Total charge enclosed in terms of algebraic sum. Let q1, q2, q3 …. ,charges are present in a region then the total force on a particular charge is the vector sum of forces that it experience due to for a system of three charges the force on q3 due to charges q1 and q2 will be

Electric potential at any point in a region of electric field is defined as the work done in carrying a unit positive charge from

S.I unit = J/C or volt (V) scalar quantity.

potential at a point due to charged particle: Let we bring, a test charge q

in the field of charge q placed a point O. The repulsive force experienced by the test charge

, a small distance dx.

⇒ dW= Fdx

The total work done, in displacing a distance x

= ⇒

We know that electric potential is given by

=

Electric potential diference between two points in an electric field is defined as the amount of workdone per unit positive charge in moving it from one point to other against the

=

Euipotential Surface is a surface on which the potential have the same value at all points. In the other words the potential two points on a equipotential nsurface is zero

Electric field lines are always perpendicular to an

. charges are present in a region then the total force on a particular charge is the vector sum of forces that it experience due to

Let we bring, a test charge q0 from infinity to experienced by the test charge

=

Electric potential diference between two points in an electric field is defined as the amount of workdone per unit positive charge in moving it from one point to other against the

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Ohm’s Law:-

If there is no change in the physical state of conductor (such as length, thickness, temperature), then ratio of potential difference applied across its ends and current flowing

through it, is constant.

=

Limitations:

It is valid for metal conductors provided temperature and other physical conditions remain constant.

The resistance of the material changes with temperature. It is not applicable for a gaseous conductor.

It is not applicable to semiconductors like germanium and silicon.

Ampere’s Law:-

Ampere’s Circuital Law states the relationship between the current and the magnetic field created by it.

This law states that the integral of magnetic field density (B) along an imaginary closed path is equal to the product of current enclosed by the path and permeability of

the medium. ∮ . =

Biot savart’s Law:-

the magnetic flux density of which dB, is directly proportional to the

 length of the element dl,

 the current I,

 the sine of the angle (sinθ), between direction of the current and the vector joining a given point of the field and the current element and

 is inversely proportional to the square of the distance of the given point from the current element, r.

= 4

This is Biot Savart law statement. Here, μ0 used in the expression of constant k is absolute permeability of air or vacuum and it's value is 4π10-7 Wb/ A-m

Fraday’s Law:-

(i) When ever the linked flux through a coil is changed, an emf is induced. (ii) The magnitude of the induced emf is equal to the rate of change of the linked flux

=

Example: Magnetic Field Of A Solenoid

A solenoid consists of a helical winding of wire on a cylinder, usually circular in cross section. If the solenoid is long in comparison with its cross-sectional diameter and the coils are tightly wound, the internal field near the midpoint of the solenoid’s length is very nearly uniform over the cross section and parallel to the axis, and the external field near the midpoint is very small. Use Ampere’s law to find the field at or near the center of such a long solenoid. The solenoid has n turns of wire per unit length and carries a current I.

From Ampere’s Law, we have: ∮B .dl =μ0Iencl Following the integration path, we have:

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∮ . = 0

. + . + . + . = + 0 + 0 + 0 =

=

Example: Magnetic Field of A Toroidal Solenoid

The figure shows a doughnut-shaped toroidal solenoid. Solenoid is bided with N turns of wire, each carrying a current I. We have to find the magnetic field at all points.

From Ampere’s Law, we have:

∮ . =

Let’s consider path 1: No current is enclosed by the path. Hence, B = 0. Let’s consider path 3: No current is enclosed by the path. Hence, B = 0.

Let’s consider path 2: B×2πr = μ0NI ⇒ B = μ0NI/(2πr)

Ex. 1. Determine the magnetic field strength a distance r away from an infinitely long current carrying wire using the Ampere's law.

Answer: From the Ampere's law, we solve the integral

∫B.dl = B∫dl = B2πr

Then, B2πr = μoI

B = μoI / 2πr

Ex. 2. Find the current in a long straight wire that would produce a magnetic field 1.0×10 4T at a distance of 5.0 cm from the wire.

Solution: I=2πrB/μ0= 2π (5.0×10 2m)(1.0×10 4T)/4π×10 7T m/A=25 A.

Ex. 3. What is the field inside a 2.00-m-long solenoid that has 2,000 loops and carries a 1,600-A current? Solution: B= μ0nI=(4π×10 7T m/A)( 2,000/2.00 m 1)(1,600 A)=2.01 T.

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Learning Objectives

After completing this lesson you will be able to:

1. Define the following terms: vector quantity, scalar quantity. 2. Distinguish between vector and scalar quantities using examples.

3. Demonstrate an understanding of vector addition, a resultant vector and resolving a vector into components.