Electromagnetics - 2

Magnetic Field at the centre of a current carrying are
(Secondary Information):

     
=> dB =
     dB =
     B =
        , where is angle in radiam.
Therefore B at the center of a circular loop of radius R is B =


Magnetic field on the axis of a current carrying loop (Secondary Information):



Let the radius of loop be a and axial distance be z.
dB_x = dB cos
     
     
B_x
    
B_y = o

if z >> R
B =
= I = magnetic dipole moment of the loop.

Dumb Question:

Q1. What is the dimention of E/B ?
Ans: LT^-1

Q2. In the relation = q( x ), which paire are always perpendicular to each other.
Ans: (, ), (, ).


Q3. If a bean of electrons travels in a straight line m a certain region. Can we say there is no magnetic field ?
Ans: No.

Q4. Why the magnetic field along - y-axis, along the axis of a loop is zero ?
Ans: Because for every small element element which db in opposite direction.

Amphere's Law:
Similar to the Gauss's Law of electrosatics, this law provides us short cut methods of finding megnetic field in the cases of symmetry.
According to this

where is the net current crossing the area enclosed by the path.