A pair of parallel metal plates has a potential difference of 5000 V across them.
The electric field strength between them is 400 kN C^−1
. Calculate:
a the separation between the plates
b the force on a dust particle between the plates which carries a charge of 1.6 × 10^−19 C.
To calculate the separation between the plates, we can use the formula for electric field strength (E) between two parallel plates:
E = V / d
where E is the electric field strength, V is the potential difference, and d is the separation distance between the plates.
a) Rearranging the formula, we can solve for d:
d = V / E
Plugging in the given values:
V = 5000 V (potential difference)
E = 400 kN C^−1 = 400,000 N C^−1 (electric field strength)
d = 5000 V / 400,000 N C^−1
d ≈ 0.0125 meters (12.5 mm)
Therefore, the separation between the plates is approximately 0.0125 meters or 12.5 mm.
b) To calculate the force on the dust particle between the plates, we can use the formula for electric force (F) experienced by a charged particle in an electric field:
F = q * E
where F is the force, q is the charge of the particle, and E is the electric field strength.
Plugging in the given values:
q = 1.6 × 10^−19 C (charge of the dust particle)
E = 400 kN C^−1 = 400,000 N C^−1 (electric field strength)
F = (1.6 × 10^−19 C) * (400,000 N C^−1)
F ≈ 6.4 × 10^-11 N
Therefore, the force on the dust particle between the plates is approximately 6.4 × 10^-11 Newtons.