Question

In Fig. 28-55, an electron moves at speed v=100m/salong an xaxis through uniform electric and magnetic fields. The magnetic field is directed into the page and has magnitude5.00T. In unit-vector notation, what is the electric field?

Short answer

The electric field is$\overrightarrow{E}⃗=(-500V/m)\hat{j}$.

Step-by-step solution

Step 1: Identification of the given data

The speed of electron is, v=100m/s.

The magnetic field is, v=5.00T.

Understanding the concept

The electric field and magnetic field are related by the equation that ratio of magnitude of electric field and magnetic field is the velocity of that electromagnetic wave or charge. From that, we can find the electric field.

Formula:

$\frac{\left|E\right|}{\left|B\right|}=v$

Calculate the electric field in unit-vector notation

From equation 28-07, we can write
$\frac{\left|E\right|}{\left|B\right|}=v$

By substituting the value of magnetic field, we can find the electric field.

$\left|E\right|=v\left|B\right|$

Substitute all the value in the above equation.

$$\begin{gathered} \left|E\right|=5.0T\times 100m/s \\ =500V/m \end{gathered}$$

The force caused by the magnetic field is

$F_B=V\times B$

We can say that the direction of this cross product is upward or along$\hat{j}$.

To make the electron to move along a straight line, the force caused by the electric field must be equal and opposite to it. Therefore, the electric field must be downward or along $-\hat{j}$in direction.

Hence, the electric field can be written as,role="math" localid="1662820063090" $\left|E\right|=(-500V/m)\hat{j}$