A Van de Graaff generator is charged so that the magnitude of the electric field at its surface is 2.4 104 N/C. (a) What is the magnitude of the electric force on a proton released at the surface of the generator? (b) Find the proton's acceleration at this instant.
Force=Eq
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To find the answers to these questions, we will use the equations that describe the electric force experienced by a charged particle in an electric field and the relationship between force and acceleration.
(a) The magnitude of the electric force experienced by a charged particle in an electric field is given by the equation:
F = q * E,
where F is the electric force, q is the charge, and E is the electric field.
In this case, the charged particle is a proton, which has a charge of +1.6 x 10^(-19) C. The given magnitude of the electric field at the surface of the generator is 2.4 x 10^4 N/C.
Plugging in the values into the equation, we have:
F = (1.6 x 10^(-19) C) * (2.4 x 10^4 N/C)
Calculating this, we get:
F = 3.84 x 10^(-15) N
The magnitude of the electric force on the proton released at the surface of the generator is 3.84 x 10^(-15) N.
(b) The acceleration of the proton can be found using Newton's second law, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration:
F = m * a,
where F is the force, m is the mass, and a is the acceleration.
The mass of a proton is approximately 1.67 x 10^(-27) kg.
Rearranging the equation to solve for acceleration, we have:
a = F / m
Plugging in the values into the equation, we have:
a = (3.84 x 10^(-15) N) / (1.67 x 10^(-27) kg)
Calculating this, we get:
a ≈ 2.30 x 10^12 m/s^2
The proton's acceleration at this instant is approximately 2.30 x 10^12 m/s^2.
To answer these questions, we need to use the given information and apply some principles of electrostatics. Let's break it down step by step:
(a) To find the magnitude of the electric force on a proton released at the surface of the generator, we can use the equation for the electric force:
Electric force (F) = Charge (q) * Electric field strength (E)
We know the electric field strength (E) is 2.4 * 10^4 N/C and the charge of a proton (q) is the elementary charge (e) which is approximately 1.6 * 10^-19 coulombs.
F = q * E
F = (1.6 * 10^-19 C) * (2.4 * 10^4 N/C)
By calculating this equation, we can find the magnitude of the electric force on the proton.
(b) To find the proton's acceleration at this instant, we'll use Newton's second law:
Force (F) = Mass (m) * Acceleration (a)
From part (a), we know the magnitude of the electric force (F) on the proton. The mass of a proton (m) is approximately 1.67 * 10^-27 kilograms.
F = m * a
a = F / m
By substituting the value of the force and mass into this equation, we can find the acceleration of the proton.
Remember to perform the calculations using the appropriate units and round off the final answers to the appropriate number of significant figures.