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An electron is moving with a velocity (2...

An electron is moving with a velocity `(2 hat(i) + 2hat(j))m//s` is an electric field of intensity `vec(E )= hat(i) + 2hat(j)- 8 hat(k) V//m` and a magnetic field of `vec(B)= (2 hat(j) + 3hat(k))` tesla. The magnitude of force on the electron is

A

`14.4 xx 10^(-19)N`

B

`9 xx 10^(-19)N`

C

`11.2 xx 10^(-19)N`

D

`6.4 xx 10^(-19)N`

Text Solution

Verified by Experts

The correct Answer is:
A
Here, velocity of electron `=vec(v) = 2 hat(i)+ 2hat(j)ms^(-1)`
Electric field `= vec(E )= hat(i) + 2hat(j) - 8hat(k) V m^(-1)`
Magnetic field `= vec(B) = 2hat(j) + 3hat(k) T`
`:.` The Lorentz force is
`vec(F) = q (vec(E ) + vec(v) xx vec(B))`
`=(-1.6 xx 10^(-19)) [hat(i) + 2hat(j) -8hat(k) + (2hat(i) + 2hat(j)) xx (2hat(j) + 3hat(k))]`
`=(-1.6 xx 10^(-19)) [hat(i) + 2hat(j) - 8hat(k) + 4hat(k) - 6hat(j) + 6hat(i)]`
`=(-1.6 xx 10^(-19)) [7 hat(i) - 4hat(j) - 4hat(k)]`
`|vec(F)| = 1.6 xx 10^(-19) xx 9 = 14.4 xx 10^(-19)N`
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