Physics 9702 · AS & A Level · Potential difference and power

Potential difference and power — practice question

A p.d. of $2.5\,\text{kV}$ is set across two horizontal metal plates in a vacuum, as illustrated in Fig. 2.1. Each plate measures $5.9\,\text{cm}$ in length and the gap between them is $4.0\,\text{cm}$. This setup gives a uniform electric field between the plates. Assume the field does not spread past the plate edges. An electron enters the field at point A with horizontal speed $3.7 \times 10^7\,\text{m s}^{-1}$ along the midpoint between the plates, and it exits at point B.
(a)[1]

Define electric field strength in words.

(b(i))[1]

Calculate the time required for the electron to travel from A to B.

(b(ii))[2]

Calculate the size of the electric field strength.

(b(iii))[2]

Show that the electron’s acceleration in the field is $1.1 \times 10^{16}\,\text{m s}^{-2}$.

(b(iv))[3]

Use the acceleration from (iii) together with your answer to (i) to find the vertical distance $y$ between point B and the upper plate.

(b(v))[1]

Explain why the calculation in (iv) does not need to include the gravitational effects on the electron.

(b(vi))[2]

At time $t = 0$, the electron enters the field. On Fig. 2.2, sketch graphs to show how, with time $t$, (1) the horizontal component $v_x$ of the electron’s velocity, and (2) the vertical component $v_y$ of the electron’s velocity vary. You do not need numerical values.

(c(iv))[3]

Use the acceleration from (iii) along with your answer to (i) to find the vertical distance $y$ from point B to the upper plate.

(c(v))[1]

Explain why the electron’s gravitational effect can be omitted from the calculation in (iv).

(c(vi))[2]

At $t = 0$, the electron enters the field. On Fig. 2.2, sketch graphs to show how the horizontal component $v_x$ of the electron’s velocity and the vertical component $v_y$ of the electron’s velocity vary with time $t$. No numerical values are needed.

Worked solution & mark scheme

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