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The potential difference, also known as voltage, is a measure of the work needed to move a charge from one point to another in an electric field. It is essentially the energy required per unit charge to move across a certain distance.
In practical terms, think of potential difference as the electric 'pressure' that pushes charges through an electric field.

• It's measured in volts (V).
• One volt is equivalent to one joule per coulomb.

The potential difference is crucial in many devices, like cathode ray tubes (CRTs), where it accelerates electrons across the tube.

In our exercise, we use potential difference to generate an electric force strong enough to counteract the gravitational force on an electron. This balance allows it to remain stationary instead of succumbing to gravity.

Gravitational force is a fundamental force that attracts any objects with mass towards each other. It's most noticeable when we consider the weight of objects on Earth's surface.

• This force can be calculated using the formula: \( F_g = m \times g \).
• Here, \( m \) is the mass of an object and \( g \) is the acceleration due to gravity, approximately \( 9.8 \, \text{m/s}^2 \) on Earth.

For an electron, although it is incredibly small with a mass of \( 9.11 \times 10^{-31} \text{ kg} \), it still experiences gravitational force.

When a force, like gravity, acts on an electron, it naturally accelerates in the direction of the force unless counteracted by another force, like an electric field.

In a CRT, electrons are accelerated using electric potential difference. Acceleration is the rate of change of velocity of an object and is influenced by forces acting on that object.
For electrons, the acceleration involves both the gravitational force and the electric force created by the potential difference.

• Electrons accelerate faster towards positively charged areas because they are negatively charged themselves.
• Their acceleration can be quantified using \( F = m \times a \), where \( F \) is the net force acting on the electron.

This equation is crucial for understanding how CRTs work, as it helps us calculate how much voltage is needed to fire electrons towards the screen, forming images.

In our problem, the potential difference creates an electric field strong enough to make the electron's net acceleration zero, keeping it stationary.

Coulomb's Law is a principle describing the force between two charges.
It states that the force between two point charges is proportional to the product of their charges and inversely proportional to the square of the distance between them.

• This law mathematically is: \( F = k \frac{|q_1 \times q_2|}{r^2} \).
• Where \( k \) is Coulomb's constant, \( q_1 \) and \( q_2 \) are charges, and \( r \) is the distance between the charges.

Understanding this law is fundamental in physics because it helps explain how electric forces are calculated, which is essential in dealing with electrons in CRTs.

In our context, though Coulomb's Law isn't directly used to calculate the potential difference, its principle underlies the interactions within the electric field, affecting how strongly the field can push the electrons against gravity.