Magnetic Force

  Magnetic Force

The magnetic field B is defined from the Lorentz Force Law, and specifically from the magnetic force on a moving charge:

The implications of this expression include:

1.     The force is perpendicular to both the velocity v of the charge q and the magnetic field B.

2.     The magnitude of the force is F = qvB sinθ where θ is the angle < 180 degrees between the velocity and the magnetic field. This implies that the magnetic force on a stationary charge or a charge moving parallel to the magnetic field is zero.

3.     The direction of the force is given by the right hand rule. The force relationship above is in the form of a vector product.

From the force relationship above it can be deduced that the units of magnetic field are Newton seconds /(Coulomb meter) or Newtons per Ampere meter. This unit is named the Tesla. It is a large unit, and the smaller unit Gauss is used for small fields like the Earth's magnetic field. A Tesla is 10,000 Gauss. The Earth's magnetic field is on the order of half a Gauss.

Direction of force

Direction of force

The direction of force is determined by the above equations, in particular using the right-hand rule to evaluate the cross product. Equivalently, one can use Fleming's left hand rule for motion, current and polarity to determine the direction of any one of those from the other two, as seen in the example. It can also be remembered in the following way. The digits from the thumb to second finger indicate 'Force', 'B-field', and 'I(Current)' respectively, or F-B-I in short. Another similar trick is the right hand grip rule.

Force on current-carrying wire

           Force on current-carrying wire

A straight, stationary wire carrying an electric current, when placed in an external magnetic field, feels a force. This force is the result of the Lorentz force (see above) acting on each electron (or any other charge carrier) moving in the wire. The formula for the total force is as follows:

where

F = Force, measured in newtons

I = current in wire, measured in amperes

B = magnetic field vector, measured in teslas

    = vector cross product

L = a vector, whose magnitude is the length of wire (measured in metres), and whose direction is along the wire, aligned with the direction of conventional current flow.

Alternatively, some authors write

where the vector direction is now associated with the current variable, instead of the length variable. The two forms are equivalent

If the wire is not straight but curved, the force on it can be computed by applying this formula to each infinitesimal segment of wire, then adding up all these forces via integration.

The Lorentz force on a macroscopic current is often referred to as the Laplace force.

Force due to a Magnetic Field

  Force due to a Magnetic Field

 Force on a charged particle

Charged particle drifts in a homogenous magnetic field. (A) No disturbing force (B) With an electric field, E (C) With an independent force, F (eg. gravity) (D) In an inhomgeneous magnetic field, grad H

where

F is the force (in newtons)

q is the electric charge of the particle (in coulombs)

v is the instantaneous velocity of the particle (in metres per second)

B is the magnetic field (in teslas)

and × is the cross product.

Electric convection current

Electric convection current

where ρ is electric charge density.  was seen as a kind of magnetic current of vortices aligned in their axial planes,  with  being the circumferential velocity of the vortices. With µ representing vortex density, we can now see how the product of µ with vorticity  leads to the term magnetic flux density which we denote as.

The electric current equation can be viewed as a convective current of electric charge that involves linear motion. By analogy, the magnetic equation is an inductive current involving spin. There is no linear motion in the inductive current along the direction of the   vector. The magnetic inductive current represents lines of force. In particular, it represents lines of inverse square law force.

The extension of the above considerations confirms that where  is to, and where is to ρ, then it necessarily follows from Gauss's law and from the equation of continuity of charge that  is to. i.e.  parallels with , whereas  parallels with .

In SI units,  and are measured in teslas (T) and amperes per metre (A/m), respectively; or, in cgs units, in gauss (G) and oersteds (Oe), respectively. Two parallel wires carrying an electric current in the same direction will generate a magnetic field that will cause a force of attraction between them. This fact is used to define the value of an ampere of electric current.

The fields  and  are also related by the equation

        (SI units)

  (cgs units), where  is magnetization.

MAGNETIC FIELD Definition

Definition

Magnetic fields are produced by electric currents, which can be macroscopic currents in wires, or microscopic currents associated with electrons in atomic orbits. The magnetic field B is defined in terms of force on moving charge in the Lorentz force law. The interaction of magnetic field with charge leads to many practical applications. Magnetic field sources are essentially dipolar in nature, having a north and south magnetic pole. The SI unit for magnetic field is the Tesla, which can be seen from the magnetic part of the Lorentz force law Fmagnetic = qvB to be composed of (Newton x second)/(Coulomb x meter). A smaller magnetic field unit is the Gauss (1 Tesla = 10,000 Gauss).

UNDERSTAND THE CONCEPTS OF CAPACITANCE AND DETERMINE CAPACITANCE VALUES IN DC CIRCUITS

Magnetic Field

In physics, a magnetic field is a field that permeates space and which exerts a magnetic force on moving electric charges and magnetic dipoles. Magnetic fields surround electric currents, magnetic dipoles, and changing electric fields.

When placed in a magnetic field, magnetic dipoles align their axes to be parallel with the magnetic field, as can be seen when iron filings are in the presence of a magnet (see picture at right). Magnetic fields also have their own energy and momentum, with an energy density proportional to the square of the field intensity. The magnetic field is typically measured in either teslas (SI units) or gauss (cgs units).

There are some notable specific incarnations of the magnetic field. For the physics of magnetic materials, see magnetism and magnet, and more specifically ferromagnetism, paramagnetism, and diamagnetism. For constant magnetic fields, such as are generated by stationary dipoles and steady currents, see magnetostatics. For magnetic fields created by changing electric fields, see electromagnetism.

The electric field and the magnetic field are closely interlinked due to Einstein's theory of special relativity (see relativistic electromagnetism). Together, they make up the electromagnetic field.

aircraft engineering design Assignment answer

Customer Specification:

Task 1
Prepare a design specification containing the major design parameters as a machine tools designer.

Performance: The screw driver should be able to drive wooden screw and/or slotted machine screw of size: (7/16inches or 11mm).  Its handle should have proper shape to fit the palm of user hand with proper grip. Blade should access places with narrow spaces.

Environment: Since it will be multitasking and used by the skilled workers its materials should be capable of operating in standard atmosphere as well as in dusty, oily environment. Also it should be less sensitive to change of temperature. The screwdriver is most likely not to be used in electrical apparatus and appliances.

Maintenance: The maintenance of the screwdriver should be as simple as possible. Proper methodology for keeping the correct angle of the blade should be maintained.
Cost: The price should not exceed $10

Quantity: Total 500pieces.

Aesthetic/Ergonomics: The Screwdriver should be gripped easily and the worker should be comfortable to use it. The finishing work should be done neatly so that there is minimum chance of corrosion and rusting.

Size/Weight: The weight of the screwdriver should not exceed 0.5lbs and should maintain standard size requirement laid by British Standards for Screwdriver and Accessories.
Safety: The screwdriver must sustain standard torque requirement & should not damage the screw slot. The material used in the screwdriver should not be hazardous. Associated HSE guidance should be complied with.

engineering Design Assignment system

ASSIGNMENT (OUTCOME 1&2)
Engineering Design

Outline a customer specification for the cabinet screwdriver containing essential requirements specified in customer brief. (L1.1)

List all the major design parameters required in the design process of Cabinet Screw driver. The parameters must meet BS2559-1994 design standards. Prepare a design specification for the cabinet screwdriver. (L1.2 & L 1.3).

Provide suitable documentation demonstrating that the design specification meet all the essential customer requirements. (L1.4)

Analyze the design specification and propose at least three possible design variations for the cabinet screwdriver. (L2.1)

Evaluate each of the possible design variation and enlist all the important features related to the design respectively. (D3)

Summarize all the essential design parameters for the proposed design variants mentioned in task 2.2. (L2.2)

Use suitable analyzing technique to obtain the optimum design solution from the proposed design variations. (L2.3)

Appraise the reasons for the selection of optimum solution. Demonstrate that effective judgment has been made and valid conclusion has been achieved. (M1).

Assess all the essential parameters involved in the design process for the optimum cabinet screw driver which you have designed. And present the optimum design solution using the appropriate CAD tools. (D1)

Use appropriate design review method that demonstrates optimum conceptual design for cabinet screwdriver meets all the essential customer requirements. (L2.4)

Prepare a design report containing all the relevant parameters factors associated with the design process of Cabinet Screwdriver. (L2.5)

List all the activities which you have performed during the design process and how you have effectively managed all the risk associated with design procedure. (D2).  

Deliver a 5minutes presentation summarizing all the essential requirements  and design steps involved in the design process.(M3)

engineering Design Assignment system

ASSIGNMENT (OUTCOME 1&2)
Engineering Design

Outline a customer specification for the cabinet screwdriver containing essential requirements specified in customer brief. (L1.1)

List all the major design parameters required in the design process of Cabinet Screw driver. The parameters must meet BS2559-1994 design standards. Prepare a design specification for the cabinet screwdriver. (L1.2 & L 1.3).

Provide suitable documentation demonstrating that the design specification meet all the essential customer requirements. (L1.4)

Analyze the design specification and propose at least three possible design variations for the cabinet screwdriver. (L2.1)
Evaluate each of the possible design variation and enlist all the important features related to the design respectively. (D3)
Summarize all the essential design parameters for the proposed design variants mentioned in task 2.2. (L2.2)
Use suitable analyzing technique to obtain the optimum design solution from the proposed design variations. (L2.3)
Appraise the reasons for the selection of optimum solution. Demonstrate that effective judgment has been made and valid conclusion has been achieved. (M1).
Assess all the essential parameters involved in the design process for the optimum cabinet screw driver which you have designed. And present the optimum design solution using the appropriate CAD tools. (D1)

Use appropriate design review method that demonstrates optimum conceptual design for cabinet screwdriver meets all the essential customer requirements. (L2.4)

Prepare a design report containing all the relevant parameters factors associated with the design process of Cabinet Screwdriver. (L2.5)
List all the activities which you have performed during the design process and how you have effectively managed all the risk associated with design procedure. (D2).  

Deliver a 5minutes presentation summarizing all the essential requirements  and design steps involved in the design process.(M3)