Question

What is meant by crossed electric and magnetic fields? Under what condition a charged particle entering a crossed electric and magnetic field passes undeflected?

Answer 1

Hint: In this question we will use the basic concept of electric field and magnetic field. We will also use the Lorentz force formula to figure out whether a particle gets undeflected. We have to check the effect of both forces in the electric and magnetic field.

Complete step-by-step answer:
Electric field and magnetic field which are uniform and are perpendicular to each other which is called crossed electric and magnetic field. Perpendicular arrangement of both the fields are also called velocity selector. Magnetic force is countered by electric force in z-direction. Initially charge is at rest in crossed fields. Particle which is in the electric and magnetic field and the force which is acted on it is the Lorentz force. The formula for Lorentz force is:
\[\overrightarrow{F}=q\left( \overrightarrow{E}+\overrightarrow{v}\times \overrightarrow{B} \right)\]
Where
\[\begin{align}
  & F=force \\
 & q=ch\arg e \\
 & E=electric\ field \\
 & v=velocity \\
 & B=magnetic\ field \\
\end{align}\]
The Hall Effect further explains that when the magnetic field is perpendicular to the electric field it will result in the deflection and separation of ions in the area around us. Moving charges produce a magnetic field. If the direction of a charged particle is either parallel or anti-parallel to the field then the force is zero, and the force is maximum when charge moves perpendicular to the field. A Charged particle will get undeflected when an electric field is switched off in a region of crossed electric and magnetic field but if the magnetic field is switched off instead of electric field the particle will have initial acceleration.
Torque is the measure of how much force is acted on an object and which makes an object rotate about an axis. It is also known as pulling power and is also called moment of force about an axis. When a particle is travelling in a straight line then electric and magnetic force gets balanced. A particle will be undeflected, if it will travel with a velocity which is equals to
\[V=\dfrac{E}{B}\].

Note: Magnet has attractive and directive properties. Monopoles do not exist. Magnets are the key to special relativity. The magnetic fields are strongest at poles and weaker at centre Magnetic field lines starting from the North Pole and end to South Pole outside the magnet.