Electric Fields and Particle Dynamics Study Guide

In a vacuum environment, two charged metal plates are positioned exactly $15\,cm$ ( $0.15\,m$ ) apart.
A uniform electric field exists between these plates with a strength ( $E$ ) of $3000\,NC^{-1}$ .
An electron is released from rest ( $u = 0$ ) at point P, which is located just outside the negative plate.
The electric force ( $F_e$ ) acting on the electron is calculated using the formula $F = qE$ . Given the charge of an electron is $-1.6 \times 10^{-19}\,C$ , the magnitude of the force exerted is $4.8 \times 10^{-16}\,N$ .
The time interval ( $t$ ) required for the electron to travel the distance between the plates and reach the positive plate is $2.39 \times 10^{-8}\,s$ .
The final velocity ( $v$ ) of the electron just before it impacts the positive plate is $12.6 \times 10^{6}\,ms^{-1}$ (also noted as $1.26 \times 10^7\,ms^{-1}$ ).

A tiny ball with a mass ( $m$ ) of $0.60\,g$ ( $6.0 \times 10^{-4}\,kg$ ) is attached to the end of a thread.
The ball is placed within a horizontal electric field with a strength of $700\,NC^{-1}$ .
The system reaches equilibrium when the thread makes an angle of $20^{\circ}$ with the vertical.
The forces acting on the ball are divided into horizontal and vertical components:
- The vertical component of tension ( $T \cos(20^{\circ})$ ) balances the weight of the ball ( $mg$ ).
- The horizontal component of tension ( $T \sin(20^{\circ})$ ) balances the electric force ( $F_e = qE$ ).
Based on these equilibrium conditions, the magnitude of the charge ( $q$ ) on the ball is determined to be $3.06 \times 10^{-6}\,C$ , and the sign of the charge is positive ( $+ve$ ).

An electron beam is directed between deflecting plates where the electric field strength ( $E$ ) is $10^5\,Vm^{-1}$ .
Constants for these calculations include:
- Charge of an electron ( $e$ ): $-1.6 \times 10^{-19}\,C$ .
- Mass of an electron ( $m_e$ ): $9.1 \times 10^{-31}\,kg$ .
The electric force ( $F_e$ ) acting on a single electron in this beam is $1.6 \times 10^{-14}\,N$ .
The weight ( $W$ ) of the electron is negligible compared to the electric force. The ratio of the electric force to the weight ( $F_e / W$ ) is approximately $1.794 \times 10^{15}$ .
The resulting acceleration ( $a$ ) of each electron due to the electric field is $1.758 \times 10^{16}\,m/s^2$ .

A configuration involves charges of $+8\,\mu C$ and $-5\,\mu C$ relative to a specific point P.
Point P is located at a distance of $5\,cm$ from the charges.
The calculated electric field strength at point P is $900,000\,N/C$ .
The region where the total electric field would be zero is identified at a distance of $0.036\,m$ from a reference point.
If a test charge of $-40\,nC$ is placed exactly at point P, the magnitude of the force acting on that test charge is $0.036\,N$ . The direction of this force is towards the left.

Three charges are positioned at three corners of a square, with each side measuring $30.0\,cm$ ( $0.30\,m$ ).
The specific charges located at the corners are:
- $Q_1 = -4\,\mu C$
- $Q_2 = -5\,\mu C$
- $Q_3 = -50\,nC$
The electric field strength at the fourth (vacant) corner of the square is computed to be $919,318.87\,N/C$ .
If a new charge of $6.0\,\mu C$ is placed at this vacant corner, the resultant electric force acting on it is $5.52\,N$ .

An electron starts from rest in a uniform electric field with an intensity of $0.5\,kVm^{-1}$ (which is equivalent to $500\,Vm^{-1}$ ).
The field causes the electron to accelerate over a distance of $50\,mm$ ( $0.05\,m$ ).
Parameters used for calculation:
- Electron charge: $-1.6 \times 10^{-19}\,C$ .
- Electron mass: $9.1 \times 10^{-31}\,kg$ .
The acceleration ( $a$ ) experienced by the electron is $8.8 \times 10^{13}\,ms^{-2}$ .
Upon traveling the full $50\,mm$ distance, the electron reaches a final speed ( $v$ ) of $3.0 \times 10^6\,ms^{-1}$ .