An electron accelerated by a potential difference 2.5 kV moves horizontally into a region of space in which there is a downward directed uniform electric field of magnitude `10 kVm^-1.`
(a) In what direction must a magnetic field be applied so that the electron moves undeflected? Ignore the gravitational force. What is the magnitude of the smallest magnetic field possible in this case?
(b) What happens if the charge is a proton that passes through the same combination of fields ?

Explanation

To solve the problem step by step, we will break it down into parts (a) and (b) as given in the question.

### Part (a): Direction and Magnitude of the Magnetic Field

1. **Understanding the Forces**:
- An electron is moving in a horizontal direction into a region with a downward electric field of magnitude \( E = 10 \, \text{kV/m} = 10^4 \, \text{V/m} \).
- The electric force \( F_E \) acting on the electron is given by:
\[
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