Question

An electron travels with $\overrightarrow{v}=5.0\times {10}^6\hat{ı}\mathrm{m}/\mathrm{s}$through a point in space where $\overrightarrow{B}=0.10\hat{\mathrm{T}}$. The force on the electron at this point is $\overrightarrow{F}=\left(9.6\times {10}^{-14}\stackrel{˄}{i}-9.6\times {10}^{-14}\stackrel{˄}{k}\right)N$. What is the electric field?

Short answer

The electric field is $E=-5\times {10}^{5}j$

Step-by-step solution

Definition of Electromagnetic fields and Waves:

Electromagnetic fields are a combination of electric and magnetic fields of force that are both invisible. Natural events such as the Earth's magnetic field, as well as human actions, mostly through the usage of electricity, produce them.

Examples of Electromagnetic fields and Waves:

Electromagnetic fields are produced by devices such as cell phones, power cables, and computer screens.

Definition of Electron travel:

An electron is a subatomic particle with a negative charge. It can be either free (not bound to any atom) or tied to an atom's nucleus. The energy levels of electrons in atoms are represented by spherical shells of varied radii.

Given values are:

$\overrightarrow{v}=5.0\times {10}^6\hat{i}\mathrm{m}/\mathrm{s}$

$\overrightarrow{B}=0.10\hat{j}\mathrm{T}$

role="math" localid="1649999418443" $\overrightarrow{F}=\left(9.6\times {10}^{-19}\hat{i}-9.6\times {10}^{-14}\hat{k}\right)\mathrm{N}$

The formula for Force:

$\overrightarrow{F}=q\left(E+\left(v\times B\right)\right)$

Using the force formula, we have to find the value for E:

$\overrightarrow{F}=q\left(E+\left(v\times B\right)\right)$

$\frac{F}{q}=E+\left(v\times B\right)$

$E=\frac{F}{q}-\left(v\times B\right)$

$E=\frac{\left(9.6\times {10}^{-19}\hat{i}-9.6\times {10}^{-14}\hat{k}\right)}{1.6\times {10}^{-19}}-\left(5.0\times {10}^6\hat{i}\times 0.10\hat{j}\right)$

$E=-5\times {10}^{5}j$

Final answer:

The force of an Electric field is$E=-5\times {10}^{5}j$.