It is because the direction of force is always perpendicular meaning the force is always directed to the center of the circle. Deviation of charged particle in uniform magnetic field: Case 1: Suppose a charged particle enters perpendicular to the uniform magnetic field if the magnetic field extends to a distance ‘x’ which is less than or equal to radius of the path. If you look at the arrow moving away from you, you notice the tail of the arrow (represented by cross), that is moving into the screen (moving away from you). In the former case, its path results in a circular path, and in the latter case, a helical path is formed. Thus, the charged particle continues to move along the field direction with a uniform motion (a motion in which speed and velocity is constant). Helical path is formed when a charged particle enters with an angle of $\theta$ other than $90^{\circ}$ into a uniform magnetic field. But if you consider a particular instant of motion, it has a velocity vector $\vec v$. So, the magnitude of the velocity remains constant and only its direction changes. CONTACT Study Material, Lecturing Notes, Assignment, Reference, Wiki description explanation, brief detail, Motion of a charged particle in a uniform magnetic field. Particle with mass m, charge in a uniformed magnetic field Bz. Electromagnetism is all about the study of these forces (electric and magnetic forces). Note the cyclotron is just a device. A particle of charge q and mass m moves in X Y plane. In Figure 1 the magnetic field is directed inward into the screen (you are reading in the screen of a computer or a smart phone) represented by the cross (X) signs. Note that the magnetic field directed into the screen is represented by a collection of cross signs and those directed out of the screen towards you are represented dots (see Figure 2). So, the magnetic force also provides the centripetal force to the charge. From equations (2) and (3), it is evident that the angular frequency and period of rotation of the particle in the magnetic field do not depend upon (i) the velocity of the particle and (ii) radius of the circular path. For example you can hold ionized gas of very high temperature such as $10^6 \text{K}$ in a magnetic bottle which can destroy any material if comes in contact with such a high temperature. MECHANICS Now we want to answer this question: why do charged particles move in a helical path? (BS) Developed by Therithal info, Chennai. (2D case) When the charged particle is within a magnetic field, the radius of the circular motion is quite small and the frequency is huge. And you got, \[f = \frac{|q|B}{2\pi \, m} \tag{5} \label{5}\]. Time period of the helix is given by \begin{align*}T&=\frac{2\pi\,m}{eB}\\&=\frac{2(3.14)(9.11\times 10^{-31})}{(1.6\times 10^{-19})(0.2)}\\&=1.78\times 10^{-10}\,{\rm s}\\&=0.17\,{\rm ns}\end{align*}, Pitch of the helical motion is obtained as \begin{align*} p&=\frac{2\pi\,mv\,\cos \theta}{e\,B}\\&=\frac{2(3.14)(9.11\times 10^{-31})(1.8\times 10^{6})\cos 37^{\circ}}{(1.6\times 10^{-19})(0.2)}\\&=0.257\,{\rm mm}\end{align*}, Radius of the helical path is determined as \begin{align*}R&=\frac{mv\,\sin\theta}{eB}\\&=\frac{(9.11\times 10^{-31})(1.8\times 10^{6})\,\sin 37^{\circ}}{(1.6\times 10^{-19})(0.2)}\\&=0.193\,{\rm mm}\end{align*}. You may know that there is a difference between a moving charge and a stationary charge. In the case of $\theta=90^{\circ}$, a circular motion is created. In addition, there are hundreds of problems with detailed solutions on various physics topics. This magnetic lorentz force provides the necessary centripetal force. The Equation \eqref{5} also suggests we can change the cyclotron frequency by simply changing the magnetic field. Find the period, pitch, and radius of the helical path of the electron. Conceptual Questions At a given instant, an electron and a proton are moving with the same velocity in a constant magnetic field. Those two above motions, uniform motion parallel to the field $B$ and uniform circular motion perpendicular to the field $B$, creates the actual path of a charged particle in a uniform magnetic field $B$ which is similar to a spring and is called a spiral or helical path. The above Equation \eqref{5} suggests that the frequency of rotation does not depend on the radius of the circle and speed (linear) of the charge and it is also called cyclotron frequency.

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