the electric gun in television tube is to acelerate electrons from rest to 3×10^7m/s with in adistance of 2cm. what is electric field is required?
Eq*distance=1/2 m v^2
E= 1/2 (m/q) v^2 /distance Look up the mass of an electron (in kg), and the charge q (in Coulombs), and compute E in newtons/coulomb. distance is .02m
To calculate the electric field required, you can use the equation:
E = (ΔV) / d
Where:
E is the electric field,
ΔV is the change in voltage, and
d is the distance over which the change occurs.
In this case, the change in voltage is equivalent to the kinetic energy gained by the electrons, which can be calculated using the equation:
ΔV = (1/2)mv² / q
Where:
m is the mass of the electron,
v is the final velocity of the electrons, and
q is the charge of the electron.
The mass of an electron (m) is approximately 9.11 × 10^(-31) kg, and the charge of an electron (q) is approximately 1.6 × 10^(-19) C.
Given:
v = 3 × 10^7 m/s,
d = 2 cm = 0.02 m,
m ≈ 9.11 × 10^(-31) kg,
q ≈ 1.6 × 10^(-19) C.
1. Calculate ΔV using the equation: ΔV = (1/2)mv² / q
ΔV = (1/2)(9.11 × 10^(-31) kg)(3 × 10^7 m/s)² / (1.6 × 10^(-19) C)
2. Simplify the equation:
ΔV ≈ (1/2)(9.11 × 10^(-31) kg)(9 × 10^14 m²/s²) / (1.6 × 10^(-19) C)
3. Calculate ΔV:
ΔV ≈ 2.04675 V
4. Now, substitute the values of ΔV and d into the formula: E = ΔV / d
E ≈ (2.04675 V) / (0.02 m)
5. Calculate E:
E ≈ 102.3375 V/m
Therefore, the electric field required is approximately 102.34 V/m.