Magnitude of Electric Field and Initial Proton Acceleration

In summary, we determined the magnitude of the electric field at the proton's location created by a 3.0 µC charge, using the formula F = kq1q2/d^2. We also found the initial acceleration of the proton after it is released from rest, using the formula F = ma and the known force from part a. The resulting acceleration is very large due to the strong electric field.
  • #1
liz_p88
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Homework Statement



A particle with a charge of 3.0 µC is located at rest 5.0 meters from a proton. a) Determine the magnitude of the electric field at the proton's location created by the 3.0 µC charge. b) Determine the initial acceleration of the proton after it is released from rest.

Homework Equations



a.) F/m

b.) F= ma


The Attempt at a Solution



F = 9 x 10^9 x q1 x q2 / d^2

F = 9 x 10^9 x 3 x 10^-6 x 1.6 x 10^-19 / 25 = 1.73 x 10^-16 N
 
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  • #2


a.) To determine the magnitude of the electric field, we can use the formula F = kq1q2/d^2, where F is the force between the two charges, k is the Coulomb's constant, q1 and q2 are the two charges, and d is the distance between them. In this case, q1 is the 3.0 µC charge and q2 is the charge of the proton, which is 1.6 x 10^-19 C. Plugging in the values, we get:

F = (9 x 10^9 Nm^2/C^2) x (3 x 10^-6 C) x (1.6 x 10^-19 C) / (5.0 m)^2 = 1.73 x 10^-16 N

This is the magnitude of the force between the two charges. To find the electric field at the proton's location, we divide this force by the charge of the proton, which gives us:

E = F/q2 = (1.73 x 10^-16 N) / (1.6 x 10^-19 C) = 1.08 x 10^3 N/C

Therefore, the magnitude of the electric field at the proton's location is 1.08 x 10^3 N/C.

b.) To determine the initial acceleration of the proton, we can use the formula F = ma, where F is the force between the two charges, m is the mass of the proton, and a is the acceleration. We already know the force from part a, so we can rearrange the equation to solve for a:

a = F/m = (1.73 x 10^-16 N) / (1.67 x 10^-27 kg) = 1.04 x 10^11 m/s^2

Therefore, the initial acceleration of the proton after it is released from rest is 1.04 x 10^11 m/s^2. This is a very large acceleration, which is to be expected since the electric field is quite strong due to the large charge of the 3.0 µC particle.
 

What is the magnitude of electric field?

The magnitude of electric field is a measure of the strength of an electric field at a particular point. It is defined as the force per unit charge at that point.

How is the magnitude of electric field calculated?

The magnitude of electric field can be calculated by dividing the force exerted on a charged particle by the magnitude of the charge of the particle. It can also be calculated by taking the product of the electric field strength and the distance from the source of the field.

What is the relationship between electric field and proton acceleration?

The electric field is directly related to the acceleration of a proton. The greater the electric field, the greater the acceleration of the proton. This is because the electric field exerts a force on the proton, causing it to accelerate in the direction of the field.

What factors affect the magnitude of electric field?

The magnitude of electric field is affected by the magnitude and distance of the charges creating the field, as well as the medium in which the charges are located. It is also affected by the placement and orientation of the charged particle in the field.

How does the initial velocity of a proton affect its acceleration in an electric field?

The initial velocity of a proton does not affect its acceleration in an electric field. The acceleration of a charged particle in an electric field is solely determined by the strength of the field and the charge of the particle.

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