Name: Conversion of a Galvanometer Into a Voltmeter
Uploaded: 2019-07-19
Duration: 7 min 18 s
Description: This video helps us understand the working of a galvanometer. It also teaches us how to convert it into a voltmeter of the desired range both theoretically a...

Question

Draw a schematic sketch of a cyclotron. Explain clearly the role of crossed electric and magnetic fields in accelerating the charge. Hence derive the expression for the kinetic energy acquired by the particles.

Accepted Answer

A cyclotron is a device used to accelerated positively charged particles (like $α$ -particles, deuterons etc.) to acquire enough energy to carry out nuclear disintegration etc.
It is based on the fact that the electric field accelerates a charged particle and the magnetic field keeps it revolving in circular orbits of constant frequency.
It consists of two hollow $D$ -shaped metallic chambers $D_{1}$ and $D_{2}$ called dees. The two dees are placed horizontally with a small gap separating them. The dees are connected to the source of high-frequency electric field. The whole apparatus is placed between the two poles of a strong electromagnet $N S$ as shown in fig. The magnetic field acts perpendicular to the plane of the dees and it provides the centripetal force necessary for charged particle to keep it moving in circle.
$\frac{m v^{2}}{r} = q v B \Rightarrow r = \frac{m v}{q B}$

Maximum energy gained by the charged particle

$K E_{\max} = \frac{1}{2} m v_{\max}^{2} [v_{\max} = \frac{q B r_{0}}{m}]$

$K E_{\max} = \frac{q^{2} B^{2}}{2 m} r_{0}^{2}$

where $r_{0} =$ maximum radius of the circular path followed by the positive ion.

Draw a schematic sketch of a cyclotron. Explain clearly the role of crossed electric and magnetic fields in accelerating the charge. Hence derive the expression for the kinetic energy acquired by the particles.

Important Questions on Magnetic Effect of Current

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