A charge of 5 μC moves with a speed of $2 × 10^6 m/s$ along the positive y-axis. A magnetic field $\vec B$ of strength $(2\hat i +\hat k)T$ exists in space. The magnetic force acting on the charge is :

$(-20\hat k + 10\hat i) N$

The correct answer is Option (1) → $(-20\hat k + 10\hat i) N$

Lorentz force state that,

$\vec F=q(\vec V×\vec B)$

and,

$q (charge) = +5μC$

$\vec V (velocity)=2×10^6\hat jm/s$

$\vec B(magnetic\,field)=2\hat i+\hat kT$

$\vec F=(5×10^{-6}C)×(-4×10^6\hat k×2×10^6\hat i)$

$=(10\hat i-20\hat k)N$