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 4.7 cm.
What electric field is required? The funda-
mental charge is 1.602 × 10−19 C.
Answer in units of N/C
m•a=F
m•(v²-vₒ²)/2•s=e•E
E= m•(v²-vₒ²)/2•s•e= ...
To find the electric field required to accelerate the electrons in the TV tube, we can use the following equation:
E = (m * v^2) / (2 * q * d)
where:
E is the electric field,
m is the mass of the electron (9.109 × 10^(-31) kg),
v is the final velocity of the electron (3 × 10^7 m/s),
q is the charge of the electron (1.602 × 10^(-19) C), and
d is the distance over which the acceleration occurs (4.7 cm = 0.047 m).
Plugging in the values into the formula, we get:
E = (9.109 × 10^(-31) kg * (3 × 10^7 m/s)^2) / (2 * (1.602 × 10^(-19) C) * 0.047 m)
Evaluating this expression, we find:
E ≈ 7.60 × 10^5 N/C
Therefore, the required electric field is approximately 7.60 × 10^5 N/C.