Crossed electric and magnetic fields have magnitudes of 4.65 V/m and 74.5 mT. Find the speed at which electrons moving perpendicular to both fields can travel through them without being deflected?

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**Problem: Motion of Electrons in Crossed Fields**

**Description:**

In a region of space, crossed electric and magnetic fields are present. The magnitudes of these fields are given as:

- Electric field (E): 4.65 V/m
- Magnetic field (B): 74.5 mT (millitesla)

**Question:**

At what speed can electrons move perpendicular to both fields without being deflected?

**Solution Approach:**

To find the speed at which electrons can travel through the crossed electric and magnetic fields without deflection, use the condition for zero net force: the electric force must equal the magnetic force. 

The relevant equation is:
\[ v = \frac{E}{B} \]

Where:
- \( v \) is the speed of the electrons
- \( E \) is the magnitude of the electric field (4.65 V/m)
- \( B \) is the magnitude of the magnetic field (74.5 mT converted to T for calculation)

Convert B to Tesla:
\[ 1 \text{ mT} = 10^{-3} \text{ T} \]
\[ B = 74.5 \text{ mT} = 74.5 \times 10^{-3} \text{ T} \]

Substitute known values into the formula to find \( v \).
Transcribed Image Text:**Problem: Motion of Electrons in Crossed Fields** **Description:** In a region of space, crossed electric and magnetic fields are present. The magnitudes of these fields are given as: - Electric field (E): 4.65 V/m - Magnetic field (B): 74.5 mT (millitesla) **Question:** At what speed can electrons move perpendicular to both fields without being deflected? **Solution Approach:** To find the speed at which electrons can travel through the crossed electric and magnetic fields without deflection, use the condition for zero net force: the electric force must equal the magnetic force. The relevant equation is: \[ v = \frac{E}{B} \] Where: - \( v \) is the speed of the electrons - \( E \) is the magnitude of the electric field (4.65 V/m) - \( B \) is the magnitude of the magnetic field (74.5 mT converted to T for calculation) Convert B to Tesla: \[ 1 \text{ mT} = 10^{-3} \text{ T} \] \[ B = 74.5 \text{ mT} = 74.5 \times 10^{-3} \text{ T} \] Substitute known values into the formula to find \( v \).
Expert Solution
Step 1: Formula

The electron will move undeflected when the force on the electron due to the electric field will be equal to the Lorrentz force. Hence, 

q E equals q v B

Hence, 

v equals E over B

is the velocity of the electron such that it moves undeflected. 

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