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A charged particle of charge 2*0muC movi...

A charged particle of charge `2*0muC` moving along x-axis with a speed of `3xx10^6ms^-1` enters a magnetic field, `vecB=(0*3hatj+0*4hatk)` tesla acting in a specific. What is the magnitude of magnetic force on the charged particle?

Text Solution

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Here, `q=2*0muC=2xx10^-6C`,
`vecv=(3xx10^6hati)ms^-1`
`B=(0*3hatj+0*4hatk)T`
Magnetic force on the charged particle is
`vecF=q(vecvxxvecB)`
`=(2xx10^-6)[(3xx10^6)hatixx(0*3hatj+0*4hatj)]`
`=(2xx10^-6)xx10^6[3hatixx(0*3hatj+0*4hatk)]`
`=2[(3xx0*3)(hatixxhatj)+3xx0*4(hatixxhatk)]`
`=2[0*9hatk-1*2hatj]=[1*8hatk-2*4hatj]`
`:.` Magnitude of magnetic field is
`|vecF|=sqrt((1*8)^2+(-2*4)^2)`
`=sqrt(3*24+5*76)=3*0N`
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