In the product
\(\vec{F} = q(\vec{v} \times \vec{B})\)
= \(q\vec{v}\times (B\hat{i}+ B\hat{j}+B_0\hat{k})\)
For q = 1 and \(\vec{v}= 2\hat{i}+ 4\hat{j}+6\hat{k})\) and
\(\vec{F}= 4\hat{i}- 20\hat{j}+12\hat{k})\)
What will be the complete expression for
(1) \(-8\hat{i}- 8\hat{j} - 6\hat{k})\)
(2) \(-6\hat{i}- 6\hat{j} - 8\hat{k})\)
(3) \(-8\hat{i}+ 8\hat{j} - 6\hat{k})\)
(4) \(6\hat{i}+6\hat{j} - 8\hat{k})\)
Correct answer: (2) \(-6\hat{i}- 6\hat{j} - 8\hat{k})\)
Explanation:
\(\vec{F} = q(\vec{v} \times \vec{B})\)
\(4\hat{i}- 20\hat{j} +12\hat{k}\) = 1\(\begin{vmatrix}
i & j & \hat{k} \\[0.3em]
2 & 4 & 6 \\[0.3em]
B & B & B_0
\end{vmatrix}\)
Comparing
⇒ 4 = 4B0 - 6B
-20 = -2B0 + 6B
12 = 2B - 4B
Solving B = -6
B0 = -8
∴ \(\vec{B} = -6\hat{i}- 6\hat{j} - 8\hat{k})\)