An infinitely long straight conductor carries a current of \(5~\text{A}\) as shown. An electron is moving with a speed of ${\mathrm{}}^{}$\(10^5~\text{m/s}\) parallel to the conductor. The perpendicular distance between the electron and the conductor is \(20~\text{cm}\) at an instant. Calculate the magnitude of the force experienced by the electron at that instant.

     
1. \(4\pi\times 10^{-20}~\text{N}\)
2. \(8\times 10^{-20}~\text{N}\)
3. \(4\times 10^{-20}~\text{N}\)
4. \(8\pi\times 10^{-20}~\text{N}\)

In the product
\(\vec{F}=q\left ( \vec{v}\times \vec{B} \right )\)
\(~~~=q\vec{v}\times \left ( B\hat{i}+B\hat{j}+B_0\hat{k} \right )\)
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 \(\vec{B}\)?
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. \(-6\hat{i}-6\hat{j}-8\hat{k}\)