An electron falls through a distance 1.5 cm in a uniform electric field of magnitude `2.0xx 10^(4) NC^(-1)` .Calculate the time it takes to fall through this distance starting from rest. If the direction of the field is reversed keeping its magnitude uncharged , calculate the time taken by a proton to fall through this distance starting from rest.

Explanation

Here distance to be covered s `= 1.5 cm = 1.5 xx 10^(-2) m, ` electron field ` E= 2.0 xx 10 ^(4) N C^(-1) ` , charge on an electron /proton `=+- e= 1.6 xx 10 ^(-19) C ,` initial velocity u=0 , mass of electron m`= 9.1 xx 10 ^(-31) ` kg and mass of proton `m. =1.67 xx 10 ^(27) kg.`
Acceleration of electron in electric field a= `(F)/( m) = ( eE)/( m) `
So as per relation s=ut `+(1)/(2) at ^(2) ` , the time taken by electron to cover the distance
` " " t= sqrt(( 2s)/( a)) = sqrt(( 2sm)/( eE)) =sqrt(( 2xx( 1.5xx10^(-2))xx (9.1xx10^(-31)))/( (1.6xx 10^(-19) ) xx ( 2.0 xx10 ^(4)) ) `
`" " = 2.9xx 10 ^(-9) s `
Similarly time taken by proton t. =`sqrt(( 2sm.)/( eE) ) = sqrt(( 2xx( 1.5xx10^(-2)) xx (1.67xx10 ^(-27)))/( (1.6xx 10^(-19) ) xx ( 2.0 xx10 ^(4))) `
` " " = 1.3 xx10 ^(-7) s`