Question

An electron with an initial speed of 5.30×10⁵ m/s is brought to rest by an electric field. What is the magnitude of the electric field?

1) Cannot be determined
2) 5.30×10⁵ N/C
3) 2.65×10⁵ N/C
4) 1.06×10⁶ N/C

Answer 1

The magnitude of the electric field required to bring an electron to rest from an initial speed cannot be determined without additional information, such as the displacement over which the electron was decelerated by the electric field.

Step-by-step explanation:

The question revolves around an electron brought to rest by an electric field, requiring knowledge of physics concepts such as electric force, work-energy theorem, and fundamental electron properties.

As a starting point, we know the initial speed of the electron and that it comes to rest, implying that the kinetic energy lost by the electron equals the work done by the electric field. The work done (W) by the electric field (E) on a charge (q) over a displacement (d) is given by W = qEd. Considering the electron's charge (e) is known and is -1.60 × 10-19 C (elementary charge), we can equate the change in kinetic energy to the work done by the electric field:

qEd = ½ mv2

However, without knowing the displacement (d), we cannot calculate the exact value of the electric field strength E. Hence, the correct answer to the provided question is 1) Cannot be determined since the necessary information to calculate the electric field's magnitude is missing.