A beam of electrons is moving with constant velocity in a region having simultaneous perpendicular electric and magnetic fields of strength `20Vm^(-1)` and 0.5 T, respectively at right angles to the direction of motion of the electrons. Then, to move undeflected the velocity of electrons must be
(a) `8 m//s` (b) `20 m//s` (c) `40 m//s` (d) `(1)/(40)m//s`

Options

A. `8 m//s`
B. `20 m//s`
C. `40 m//s`
D. `(1)/(40)m//s`

Answer

To solve the problem, we need to determine the velocity of electrons such that they move undeflected in the presence of perpendicular electric and magnetic fields. The relevant relationship for this scenario is given by the equation:

\[ V = \frac{E}{B} \]

where:
- \( V \) is the velocity of the electrons,
- \( E \) is the electric field strength,
- \( B \) is the magnetic field strength.

### Step-by-Step Solution:

1. **Identify the given values:**
- Electric field strength, \( E = 20 \, \text{V/m} \)
- Magnetic field strength, \( B = 0.5 \, \text{T} \)

2. **Use the formula for velocity:**
- According to the formula, the velocity \( V \) can be calculated using:
\[ V = \frac{E}{B} \]

3. **Substitute the values into the formula:**
- Plugging in the values we have:
\[ V = \frac{20 \, \text{V/m}}{0.5 \, \text{T}} \]

4. **Perform the calculation:**
- Calculate the right-hand side:
\[ V = \frac{20}{0.5} = 40 \, \text{m/s} \]

5. **Conclusion:**
- The velocity of the electrons must be \( 40 \, \text{m/s} \) for them to move undeflected in the given electric and magnetic fields.

### Final Answer:
The correct option is (c) \( 40 \, \text{m/s} \).