In the product $\vec{F} = q(\vec{v} imes \vec{B}) = q\vec{v} imes (B\hat{i} + B\hat{j} + B_0\hat{k})$ 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 $\vec{B}$ ?

Question

In the product $\vec{F} = q(\vec{v} 	imes \vec{B}) = q\vec{v} 	imes (B\hat{i} + B\hat{j} + B_0\hat{k})$ 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 $\vec{B}$ ?

Dr. Abubacker · Accepted Answer

[Solution] $\vec{v} 	imes \vec{B} = (4B_0 - 6B)\hat{i} + (6B - 2B_0)\hat{j} - 2B\hat{k}$. Comparing: -2B = 12 gives B = -6, and $4B_0 + 36 = 4$ gives $B_0 = -8$. Answer (1).

Q. 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 $\vec{B}$ ?

Explanation

Reviewed by Dr. Abubacker

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