Force on a moving charge in a Magnetic field
In this topic Force on a moving charge in a Magnetic field , define the magnetic field and units and dimension of magnetic field .We will also know about Fleming’s left hand rule.
Before to know about this topic Force on a moving charge in a Magnetic field we must learn about Oersted’s experiment and Ampere’s swimming rule. To know about this topic click here –
Force on a moving charge in a Magnetic field –
Suppose a positive charge ‘q’ is moving with velocity ‘v’ at an angle ‘ϴ’ with magnetic field ‘B’. Then experimentally it is found that force ‘F’ experienced depends on
F α q ………(i)
F α B……………….(ii)
F α v sinϴ …………(iii)
On combining these three equations we get ,
F α q B v sinϴ
Or, F =k q B v sinϴ ; where k is constant of proportionality k=1
Then we can write F = q B v sinϴ or, F = q( x )
Here the direction of force is given by Fleming’s left hand rule or right hand screw rule .
Fleming’s left hand rule –
According to this rule when we stretch our left hand’s fore finger, middle finger and thumb such that they are perpendicular to each other , if fore finger shows the direction of field, middle finger shows the direction of current( +ve charge) then thumbs gives the direction of force .
Definition of B (magnetic field intensity) –
As we have seen in the equation F = q B v sinϴ ;
If q= 1C , v=1m/s ϴ=900 i.e. sinϴ = 1 then B= F ;
So we can define magnetic field intensity at a point is equal to the force experienced by a unit charge moving with a unit velocity perpendicular to the direction of magnetic field at that point .
Unit of magnetic field ‘B’ –
From the equation F = q B v sinϴ ,
B = F/qv sinϴ ; then unit of B is NA-1m-1 = Tesla (T) ,
And dimension of B is [M A-1 T-2]