A charge particle is moving with a velocity `3hat(i) + 4 hat(j) m//sec` and it has electric field `E = 10hat(k) N//C` at a given point. Find the magnitude of magneitc field at the same point due to the motion of the charge particle.

Options

A. `100(mu_0 varepsilon_0)`
B. `25(mu_0varepsilon_0)`
C. `12.5(mu_0varepsilon_0)`
D. `50(mu_0varepsilon_0)`

Answer

D

Explanation

`vec(E ) = (1)/(4 pi varepsilon_(0)) (q)/(r^(2)) hat(r ) = 10hat(k)`
`hat(r ) = hat(k)`
`vec(B) = (mu_(0))/(4pi) (qvec(v) xx hat(r ))/(r^(2)) = mu_(0)varepsilon_(0) {(1)/(4pivarepsilon_(o)) (q)/(r^(2))} (vec(v ) xx hat(r) )`
`|vec(B)| = |(10mu_(0)varepsilon_(0)) (vec(v) xx hat(r ))| = |(10mu varepsilon_(0)) (4hat(i) - 3hat(j))| = 50 mu_(0)varepsilon_(0)`