Ch 25: The Electric Potential

Knight Calc - Physics for Scientists and Engineers 5th Edition

Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796Not the one you use?Change textbook

Knight Calc 5th Edition

Ch 25: The Electric Potential

Problem 33

Chapter 25, Problem 33

Two small charged spheres are 5.0 cm apart. One is charged to +25 nC, the other to −15 nC. A proton is released from rest halfway between the spheres. What is the proton's speed after it has moved 1.0 cm?

Verified step by step guidance

Step 1: Calculate the electric field at the midpoint between the two spheres due to each charge. Use the formula for the electric field due to a point charge:

E = \frac{k q}{r^{2}}

, where

k

is Coulomb's constant,

q

is the charge, and

r

is the distance from the charge to the point of interest.

Step 2: Determine the net electric field at the midpoint by adding the contributions from both charges. Remember that the electric field vectors will point away from positive charges and toward negative charges, so their directions must be considered when summing.

Step 3: Calculate the force acting on the proton due to the net electric field using the formula:

F = q E

, where

q

is the charge of the proton and

E

is the net electric field.

Step 4: Use Newton's second law to find the acceleration of the proton:

a = \frac{F}{m}

, where

F

is the force and

m

is the mass of the proton.

Step 5: Use kinematic equations to calculate the proton's speed after it has moved 1.0 cm. Use the equation:

v^{2} = v^{0} + 2 a d

, where

v

is the final speed,

v 0

is the initial speed (zero in this case),

a

is the acceleration, and

d

is the distance moved (1.0 cm).

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Key Concepts

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

Coulomb's Law

Coulomb's Law describes the electrostatic force between two charged objects. It states that the force is directly proportional to the product of the magnitudes of the charges and inversely proportional to the square of the distance between them. This law is essential for calculating the forces acting on the proton due to the charged spheres.

Electric Potential Energy

Electric potential energy is the energy a charged particle possesses due to its position in an electric field. It is calculated based on the charges involved and their separation distance. Understanding how potential energy changes as the proton moves is crucial for determining its speed after moving 1.0 cm.

Kinematics and Energy Conservation

Kinematics involves the study of motion, while energy conservation principles state that the total mechanical energy in a closed system remains constant. In this scenario, the potential energy lost by the proton as it moves will convert into kinetic energy, allowing us to calculate its speed after moving a certain distance.

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Related Practice

Textbook Question

What is the electric potential at the point indicated with the dot in FIGURE EX25.31?

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Textbook Question

The two halves of the rod in FIGURE EX25.35 are uniformly charged to ±Q. What is the electric potential at the point indicated by the dot?

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Textbook Question

Two point charges qₐ and qᵦ are located on the x-axis at x=a and x=b. FIGURE EX25.36 is a graph of V, the electric potential. What is the ratio |qₐ/qᵦ|?

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Textbook Question

In a semiclassical model of the hydrogen atom, the electron orbits the proton at a distance of 0.053 nm. What is the electric potential of the proton at the position of the electron?

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Textbook Question

Four small spheres, each charged to +15 nC, form a square 2.0 cm on each side. From far away, a proton is shot toward the square along a line perpendicular to the square and passing through its center. What minimum initial speed does the proton need to pass through the square of charges?

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Textbook Question

In a semiclassical model of the hydrogen atom, the electron orbits the proton at a distance of 0.053 nm. What is the electron's potential energy?

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