Magnetic field

INTRODUCTION
Magnetic flux most often denoted as Φm, is a measure of the amount of magnetic field passing through a given surface. The magnetic flux through a given surface is proportional to the number of magnetic field lines that pass through the surface. This is the net number, i.e. the number passing through in one direction, minus the number passing through in the other direction. For a uniform magnetic field B passing through a perpendicular area the magnetic flux is given by the product of the magnetic field and the area element. The magnetic flux for a uniform B at any angle to a surface is defined by a dot product of the magnetic field and the area element vector. Where θ is the angle between B and a vector that is perpendicular (normal) to S. In the general case, the magnetic flux through a surface S is defined as the integral of the magnetic field over the area of the surface. Where is the magnetic flux, B is the magnetic field,

From the definition of the magnetic vector potential A and the fundamental theorem of the curl the magnetic flux may also be defined as: Where the closed line integral is over the boundary of the surface and dℓ is an infinitesimal vector element of that contour Σ. The magnetic flux is usually measured with a flux meter. The flux meter contains measuring coils and electronics that evaluates the change of voltage in the measuring coils to calculate the magnetic flux. Flux density is measured in Tesla (T) where 1 T = 1 Wbm-2

QUESTIONS
1. Draw the magnetic field produced by a straight wire carrying a current. Answer:

2. Copy the following diagram and mark in the polarities of the two ends of the coil. Answer:

3. Copy the following diagram and mark in the compass directions. Answer:

4. Question 4 take µo = 4π
10-7 N A-2
Calculate the magnetic flux density at the following places: (a) 2 m from a long straight wire carrying a current of 3 A
Answer:

At distance r from a long straight wire:
Magnetic flux density (B) = oI / 2r  =  3 x 10-7 T

(b) At the centre of a solenoid of 2000 turns 75 cm long when a current of 1.5 A flows Answer:

At the centre of a solenoid:
Magnetic flux density (B) = oNI / L = 5.03 x 10-3 T
5. A solenoid of length 25 cm is made using 100 turns of wire wrapped round an iron core. If the magnetic flux density produced when a current of 2 A is passed through the coil is 2.5 T calculate the permeability (µ) of the core.
Answer:

Magnetic flux density (B) = NI / L
2.5 = x 100 x 2 / 0.25  = 0.0031 T.m/A

6. A Hall probe measures a steady magnetic field directly by detecting the effect of the field on a slice of semiconductor material. A student sets up the circuit below to investigate, using a Hall probe, the factors which determine the magnetic flux density within a long solenoid.

7. Suggest and explain two ways of varying the magnitude of the flux density in the solenoid. Answer:
Factors affecting field strength are current I and spacing of coils, N coils in length L:

6 A solenoid similar to that shown in the diagram has 100 turns connected in a circuit over a length of 0.50 m. µo = 4π  10-7 N A-2. Calculate the flux density at the centre of the solenoid when a current of 10 A flows. Answer:

Magnetic flux density (B) = NI / L
=
= 2.5 mT

References:.
1. Lam Chok Sang, Lim Siang Kee. “Pre-U Text STPM Physics”, Pearson Malaysia Sdn. Bhd P.J 2. David Halliday, Robert Resnick, Jearl Walker. “Fundamentals of Physics(6th edition)”. John Wiley & Sons, Inc. (JWa, JWb). 3. Hugh D. Young, Roger A. Freedman, Lewis Ford. “University Physics(12th edition)”, Pearson Education publishings.