Name: Fleming's Left Hand Rule
Uploaded: 2019-07-19
Duration: 2 min 51 s
Description: In this video, we will look at using Fleming’s left-hand rule to help us remember how current, magnetic fields and direction go together. Get in to know more.

Question

Explain how crossed $\vec{E}$ and $\vec{B}$ fields serve as a velocity selector.

Accepted Answer

A velocity selector is an arrangement of electric and magnetic field so that the charge of a particular velocity moves undeflected in electric and magnetic field. We know that, a stationary charged particle experiences a force $(F)$ in an electric field only but a moving charged particle experiences a force both in electric $(E)$ and magnetic field $(B)$ . This is called the Lorentz force, given by:

$\vec{F} = q (\vec{E} + \vec{v} \times \vec{B})$ ....(i)

Let the electric field vector, magnetic field vector and velocity vector be mutually perpendicular as shown in the figure drawn above. Hence, these can be written as:

$\vec{E} = E \hat{j}$ ; $\vec{B} = B \hat{k}$ ; $\vec{v} = v \hat{i}$

Hence, the force due to the electric field can be written as:

${\vec{F}}_{E} = q \vec{E} = q E \hat{j}$ ......(ii)

Force due to the magnetic field can be written as:

${\vec{F}}_{B} = q \vec{v} \times \vec{B} = q (v \hat{i} \times B \hat{k}) = - q v B \hat{j}$ ....(iii)

From (ii) and (iii), it is clear that the electric and magnetic fields are opposite in direction. If the magnitude of electric and magnetic fields are so adjusted that they become equal then the total force on the charge is zero and the charge with the velocity $(v)$ will move deflected. Hence, the condition for the charge to move undeflected is:

$q E = q v B$

$\Rightarrow v = \frac{E}{B}$ .......(iv)

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