Question

Why is force perpendicular to existing magnetic field?

Answer 1

Since we're in the frame of the moving charged particle, its relative velocity is zero. Consequently the magnetic field produces no force in this frame.The force acting in a direction perpendicular to the motion of the charged particle doesn't need to be adjusted for special relativity.


Hope this helps!

Answer 2

The Force which is Perpendicular to the Magnetic field is the Magnetic Force which is same as Centripetal force..

Firstly We should know why an object move in a circular path ?
This is because of force acting on an object which is perpendicular to it towards the center of a circle in which it is moving...

Do you think..what happenes if force doesnt act perpendicular to moving object...?

If there is no firce acting perpedicular to the object , then Due to inertia of motion , Object will keep moving in same direction...

The centripetal force actually turned the particle without changing its speed while moving...

Same situation you can think...when Charge particle enters the magnetic field it starts rotating in a circle...This will happen only if there must be a force on charge particle which is acting Perpendicular to it...
This force is nothing just a Magnetic Force and this force is actually given by centipetal force...

So there is always a case when charge particle enters a magnetic field it experience force called Magnetic force acting perpendicular to the plane of Velocity and Magnetic field...Because of this force it start rotating in a circle without changing its speed...

This magnetic force is directly proportional to the following quantities :-
1 - Charge on a particle i.e q
2- Velocity of Charge particle i.e v
3- Strength or intensity of Magnetic field i.e B

so Magnetic force , F = q ( V x B ) in vector form
F = qvB (magnitude only )

Also we know that Centipetal force F = m x v^2/r
Where m = mass of charge particle
v = velocity of a charge particle
r. = Radius of a circle in which it is moving

Centripetal force is given by Magnetic force
So we must have
Centripetal force = Magnetic force
m v ^2 / r = qvB

From above relation we can find radius of a circle in which it is moving..its velocity...angular speed..and its time oeriod to complete one round of a circle...

hope this help.....