Answer
$$\vec E= ( 6\times10^{5}\;\hat i+ 1\times10^{5}\;\hat k) \;\rm V/m$$
Work Step by Step
We are given that,
- $\vec F=( 9.6\times10^{-14}\;\hat i-9.6\times10^{-14}\;\hat k)\;\rm N$
- $\vec v= ( 5\times 10^6\;\hat i)\;\rm m/s$
- $\vec B=( 0.1\;\hat j)\;\rm T$
Recalling that the net force exerted on a moving charge in an electromagnetic field is given by
$$ \vec F=q(\vec E+\vec v\times \vec B)$$
So, the net force exerted on an electron is given by
$$ \vec F=e(\vec E+\vec v\times \vec B)$$
Hence, the electric field is given by
$$\vec E=\dfrac{ \vec F}{e}-[v\times \vec B=$$
Plug the known;
$$\vec E=\dfrac{ ( 9.6\times10^{-14}\;\hat i-9.6\times10^{-14}\;\hat k)}{(-1.6\times 10^{-19})}-[( 5\times 10^6\;\hat i)\times ( 0.1\;\hat j)]$$
$$\vec E= -6\times10^{5}\;\hat i+ 6\times10^{5}\;\hat k - 5\times 10^5\;\hat k$$
$$\vec E= (- \color{red}{\bf6\times10^{5}}\;\hat i+ \color{red}{\bf1\times10^{5}}\;\hat k) \;\rm V/m$$
