Force on a moving charge in a Magnetic field

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]

 

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