The electric field at a point in space is E=(400i^+100j^)E=(400\hat{i}+100\hat{j})E=(400i^+100j^) N/C. What is the magnitude of the electron’s acceleration?

Ch 22: Electric Charges and Forces

Knight Calc - Physics for Scientists and Engineers 5th Edition

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Knight Calc 5th Edition

Ch 22: Electric Charges and Forces

Problem 29d

Chapter 22, Problem 29d

The electric field at a point in space is $E=(400$\hat{i}$+100$\hat{j}$)$ N/C. What is the magnitude of the electron’s acceleration?

Verified step by step guidance

Step 1: Recall the relationship between force and electric field. The force experienced by a charged particle in an electric field is given by the equation:

F = q E

, where

q

is the charge of the particle and

E

is the electric field vector.

Step 2: Substitute the charge of an electron into the equation. The charge of an electron is

q = - 1.6 \times 10^{-19} C

. The electric field vector is given as

E = (400 î + 100 ĵ) N / C

Step 3: Calculate the force vector. Using the equation

F = q E

, multiply the charge of the electron by each component of the electric field vector. This will give the force vector

F = (F

_î,F_ĵ).

Step 4: Use Newton's second law to find the acceleration. Newton's second law states that

F = m a

, where

m

is the mass of the electron and

a

is the acceleration. Rearrange this equation to solve for acceleration:

a = F / m

. The mass of an electron is

m = 9.11 \times 10^{-31} kg

Step 5: Calculate the magnitude of the acceleration. First, find the magnitude of the force vector using the Pythagorean theorem:

| F | = \sqrt{F}

_î2+F_ĵ2. Then, divide the magnitude of the force by the mass of the electron to find the magnitude of the acceleration:

| a | = | F | / m

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Electric Field

An electric field is a vector field surrounding electric charges that exerts a force on other charges within the field. It is represented by the symbol E and is measured in newtons per coulomb (N/C). The direction of the electric field is defined as the direction of the force it would exert on a positive test charge.

Force on a Charge

The force experienced by a charge in an electric field can be calculated using Coulomb's law, given by F = qE, where F is the force, q is the charge, and E is the electric field strength. For an electron, which has a negative charge, the force will be in the opposite direction of the electric field.

Newton's Second Law of Motion

Newton's Second Law states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass, expressed as F = ma. This principle allows us to calculate the acceleration of the electron once the force acting on it is determined from the electric field.

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The electric field at a point in space is $E = (400 \hat{i} + 100 \hat{j})$ N/C. What is the electric force on a proton at this point? Give your answer in component form.

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The electric field at a point in space is E=(400i^+100j^)E=(400\(\hat{i}\)+100\(\hat{j}\))E=(400i^+100j^) N/C. What is the magnitude of the electron’s acceleration?

Verified video answer for a similar problem:

Key Concepts

Electric Field

Force on a Charge

Newton's Second Law of Motion

The electric field at a point in space is $E=(400\(\hat{i}\)+100\(\hat{j}\))$ N/C. What is the magnitude of the electron’s acceleration?