The electron gun in a television tube
is used to accelerate electrons with mass
9.109 × 10−31 kg from rest to 3 × 107 m/s
within a distance of 2.4 cm.
What electric field is required? The funda-
mental charge is 1.602 × 10−19 C.
Answer in units of N/C
1.066 x 10^5
To find the required electric field, we can use the formula for electric field:
Electric field (E) = Force (F) / Charge (q)
In this case, we need to determine the electric field required to accelerate the electrons. The force required to accelerate an object can be calculated using Newton's second law of motion:
Force (F) = mass (m) × acceleration (a)
Given:
- Electron mass (m) = 9.109 × 10^(-31) kg
- Final velocity of the electrons (v) = 3 × 10^7 m/s
- Distance traveled (d) = 2.4 cm = 0.024 m
- Charge of an electron (q) = 1.602 × 10^(-19) C
Step 1: Calculate the initial velocity (u).
The initial velocity of the electrons is zero since they start from rest.
Initial velocity (u) = 0 m/s
Step 2: Calculate the acceleration (a).
We can use the kinematic equation:
v^2 = u^2 + 2ad
Here, v is the final velocity, u is the initial velocity, a is the acceleration, and d is the distance traveled.
Since u = 0, the equation simplifies to:
a = v^2 / (2d)
Substituting the given values:
a = (3 × 10^7 m/s)^2 / (2 × 0.024 m)
Step 3: Calculate the force (F).
Using Newton's second law, F = ma, we can substitute the mass and acceleration values:
F = (9.109 × 10^(-31) kg) × [(3 × 10^7 m/s)^2 / (2 × 0.024 m)]
Step 4: Calculate the electric field (E).
Using the formula E = F/q, we substitute the force and charge values:
E = [(9.109 × 10^(-31) kg) × (3 × 10^7 m/s)^2 / (2 × 0.024 m)] / (1.602 × 10^(-19) C)
Simplifying the expression and calculating the value of E will give you the answer in units of N/C.