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# (a) Consider a beam of charged particles moving with varying speeds.Show how crossed electric and magnetic fields can be used to select charged particles of a particular velocity ? (b) Name another device / machine do and what are the functions of magnetic and electric fields in this machine ? Where do these exists in this machine ? Write about their natures .

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A)
Solution :
Let a source S of monochrome light be placed at the focus of a convex lens $L_1$.
A parallel beam of light and lence a wavepoint gets incident on a slit AB of width d.
The incident wavefront disturbs all parts of the slit AB simultaneously .
According to Huygen's theory , all parts of the slit AB will become source of secondary wavelets spreads out it all direction , thereby causing diffraction of light after it emerges through slilt AB will become source of secondary wavelets , which all starts in the same phase .
These wavelength spread out in all direction , thereby causing diffraction of light after it emerge through slit AB .
The wave let from any two corresponding points of the two slits reach the point add constructively to produce a central bright fringe
(ii) Suppose the secondary wave lets diffected at an angle $\theta$ are focused at point P.
The secondary wavelets start ferom different parts of the slit in same phase but they reach the point P in different phases.
Draw perpendicular AN from A on to the ray B.
Then the path difference between the wavelets from A and B will be $P= BP - AP$
$\qquad= BN=AB \sin \theta=d \sin \theta$
let the point be so located on the screen that the path difference $p= \lambda$ and let the cycle $\theta-\theta_1$
$\therefore d \sin \theta_1= \lambda$
we can divide the slit AB into two halves AC and CB
the path difference between A and C will be $\large\frac{\lambda}{2}$
The condition for first dark finge is $d \sin \theta_1= \lambda$
The condition for second dark finge is $d \sin \theta_2= 2 \lambda$
$d \sin \theta _n = n \lambda$
Suppose the point p is so located that $p= 3/2 \lambda$
Condition for first secondary maximum is $d \sin \theta _2^1= \large\frac{3 \lambda}{2}$
Condition for nth secondary maximum is $d \sin \theta _n^1= (2n+1)\large\frac{ \lambda}{2}$