Two paraticles carrying equal charges move parallel to each other with the speed 150 km/s. If `F_(1)andF_(2)` are magnetic and electric forces between two charged particles then, `(|F_(1)|)/(|F_(2)|)` is `("Let "mu_(0)epsi_(0)=(1)/(9xx10^(16))S^(2)//m^(2))`

Options

A. `1.0xx10^(-6)`
B. `1.5xx10^(-7)`
C. `3.0xx10^(-6)`
D. `2.5xx10^(-7)`

Answer

D

Explanation

Given, two charge particles having same charge, q move with same speed `i.e.,v_(1)=v_(2)=150km//1.5xx10^(5)m//s`
Electric force between two moving charge particle is same as they are static,
`i.e,|F_(2)|=(1)/(4piepsi_(0)).(q^(2))/(r^(2))" ".......(i)`
Magnetic force between two moving charge particles is given by
`F=(mu_(0))/(4pi).(q_(1).q_(2)v_(1)v_(2))/(r^(2))`
`[:'q_(1)=q_(2)=qandv_(1)=v_(2)=v]`
`|F_(1)|=(mu_(0))/(4pi).(q^(2)v^(2))/(r^(2))" "......(ii)`
From Eq. (i) and (ii) we get
`:.(|F_(1)|)/(|F_(1)|)=((mu_(0))/(4pi).(q^(2)v^(2))/(r^(2)))/((1)/(4piepsi_(0)).(q^(2))/(r^(2)))=epsi_(0)mu_(0)v^(2)`
`=(1)/(9xx10^(16))xx(1.5xx10^(5))^(2)=2.5xx10^(-7)`
Hence, `(F_(1))/(F_(2))` is `2.5xx10^(-7)`.