A magnetic field of `(4.0xx10^-3hatk)T` exerts a force `(4.0hati+3.0hatj)xx10^-10N` on a particle having a charge `10^-9C` and moving in te `x-y` plane. Find the velocity of the particle.

Explanation

Magnetic force `vec(F_(m))=(4.0hat(i)+3.0hat(j))xx10^(-10)N`
Let velocity of the particle in `x-y` plane be.
`vec(v)=v_(x)hat(i)+v_(y)hat(j)` Then from the relation `vec(F)=q(vec(v)xxvec(B))` We have `(4.0hat(i)+3.0hat(j))xx10^(-10)=10^(-9)[(v_(x)hat(i)+v_(y)hat(j))xx(4xx10^(-3)hat(k))]`
`=(4v_(y)+10^(-12)hat(i)-4v_(x)xx10^(-12)hat(j))` comparing the coefficient of `hat(i)` and `hat(j)` we have,
`4xx10^(-10)=4v_(y)xx10^(-12)`
`:. v_(y)=10^(2)m//s=100m//s` and `3.0xx10^(-10)=-4v_(x)xx10^(-12)`
`:.v_(x)=075m//s :. vec(v)=-75hat(i)+100hat(j)`