Question

A certain region has an electric field $\vec{E}=(2 \hat{i}-3 \hat{j}) N / C$ and a uniform magnetic field $\vec{ B }=(5 \hat{ i }+3 \hat{ j }+4 \hat{ k }) T$. The force experienced by a charge $1 C$ moving with velocity $(\hat{ i }+2 \hat{ j }) ms ^{-1}$ is

• A. $(10 \hat{ i }-7 \hat{ j }-7 \hat{ k })$
• B. $(10 \hat{i}+7 \hat{j}+7 \hat{k})$
• C. $(-10 \hat{ i }+7 \hat{ j }+7 \hat{ k })$
• D. $(10 \hat{ i }+7 \hat{ j }-7 \hat{ k })$

Answer 1

Answer: (A)

Lorentz force, $\vec{ F }= q \{\vec{ E }+(\vec{ v } \times \vec{ B })\}$
$\vec{ v } \times \vec{ B }=\begin{vmatrix} \hat{ i } & \hat{ j } & \hat{ k } \\1 & 2 & 0 \\5 & 3 & 4\end{vmatrix}=8 \hat{ i }-4 \hat{ j }-7 \hat{ k } $
$\vec{ F }=1(2 \hat{ i }-3 \hat{ j }+8 \hat{ i }-4 \hat{ j }-7 \hat{ k })=(10 \hat{ i }-7 \hat{ j }-7 \hat{ k })$