What is the charge of a particle with a mass of 4 * 10 ^ -19 kg if it increases its speed from 10000000m / s

| March 15, 2021 | education

What is the charge of a particle with a mass of 4 * 10 ^ -19 kg if it increases its speed from 10000000m / s to 30000000m / s, passing a potential difference of 20 kV?

To find the charge of the specified particle after passing the potential difference, we use the equality: A = q * (φ1 – φ2) = ΔEk = m * ΔV2 / 2 = m * (Vk ^ 2 – Vn ^ 2) / 2, whence we express: q = m * (Vk ^ 2 – Vn ^ 2) / (2 * (φ1 – φ2)).

The values ​​of the variables: m is the mass of the specified particle (m = 4 * 10-19 C); Vк – the final velocity of the particle (Vк = 3 * 10 ^ 7 m / s); Vн – the initial velocity of the particle (Vн = 1 * 10 ^ 7 m / s); φ1 – φ2 is the potential difference passed by the specified particle (φ1 – φ2 = 20 kV = 20 * 10 ^ 3 V).

Calculation: q = m * (Vk ^ 2 – Vn ^ 2) / (2 * (φ1 – φ2)) = 4 * 10 ^ -19 * ((3 * 10 ^ 7) ^ 2 – (1 * 10 ^ 7 ) ^ 2) / (2 * 20 * 10 ^ 3) = 8 * 10 ^ -9 C = 8 nC.

Answer: The charge of the indicated particle is 8 nC.



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