If a particle of charge `10^(-12)` coulomb moving along the`hat(x)`-direction with a velocity `10^(5)m//s` experiences a force of `10^(-10)` newton in `hat(y)`-direction due to magnetic field. Then the minimum magnetic field is

Options

A. `6.25 xx 10^(3)` tesla in `hat(z)` -direction
B. `10^(-15)` tesla in `hat(z)` -direction
C. `6.25 xx 10^(-3)` tesla in `hat(z)` -direction
D. `10^(-3)` tesla in `hat(z)` -direction

Answer

D

Explanation

`q = 10^(-12)C, vec(v) = 10^(5) hat(i) m//sec, vec(F) = 10^(-10) hat(j) N`
`F = B q v sin theta`
`B = (F)/(q v sin theta)`
for `B` to be minimum, `theta = 90^(@)`
`B_(min) = (F)/(qv) = (10^(-10))/(10^(-12) xx 10^(5)) = 10^(-3)T`
`vec(F) = q vec(v) xx vec(B)`
`vec(v) xx vec(B)` is along `+y` direction, for this `vec(B)` should be along `-Z` direction
`hat(i) xx (- hat(k)) = hat(j)`