Electric fields：練習問題

Which statement correctly defines the electric field strength at a point?

Two point charges \(+Q\) and \(+16Q\) are placed a distance \(L\) apart in a vacuum. A third charge \(q\) is placed at a point on the line joining the two charges such that the resultant electric force on it is zero.
What is the distance of this point from the charge \(+Q\)?

A proton and an \(\alpha\)-particle are both accelerated from rest through the same potential difference \(V\) in a vacuum.
What is the ratio \(\frac{\text{final momentum of } \alpha\text{-particle}}{\text{final momentum of proton}}\)?

A particle with charge +q and mass m is placed at rest in a uniform electric field of strength E. Derive an expression for the time t required for the particle to travel a distance L in the direction of the field.

(a) Define electric field strength at a point.
(b) A uniform electric field is produced between two horizontal parallel metal plates. The plates have a length of \( 6.0 \, \text{cm} \) and are separated by a distance of \( 2.5 \, \text{cm} \) in a vacuum. A potential difference of \( 500 \, \text{V} \) is applied across the plates. An electron enters the region between the plates halfway between them, travelling horizontally with a speed of \( 1.2 \times 10^7 \, \text{m s}^{-1} \).
(i) Calculate the magnitude of the electric field strength between the plates.
(ii) Calculate the time taken for the electron to travel the length of the plates.
(iii) Determine the vertical deflection of the electron as it exits the plates.

Two point charges \( Q_A = +5.0 \, \mu\text{C} \) and \( Q_B = -3.0 \, \mu\text{C} \) are fixed in a vacuum at a distance of \( 0.20 \, \text{m} \) apart.
(a) Calculate the electric potential at the midpoint between the two charges.
(b) Determine the distance from charge \( Q_A \) along the line joining the two charges where the electric potential is zero.
(c) A third charge \( q = +2.0 \, \mu\text{C} \) is moved from infinity to the midpoint. Calculate the work done by the external agent.