Ch 26: Potential and Field

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 26: Potential and Field

Problem 2

Chapter 26, Problem 2

What is the potential difference between x_i = 10 cm and x_f = 30 cm in the uniform electric field E_x=1000 V/m?

Verified step by step guidance

Step 1: Understand the relationship between electric field and potential difference. The potential difference (ΔV) in a uniform electric field is given by the formula:

Δ V = E \cdot Δ x

, where

E

is the electric field strength and

Δ x

is the displacement in the direction of the field.

Step 2: Convert the initial and final positions from centimeters to meters, as SI units are required for calculations.

x

_i=10×10⁻2=0.1 m and

x

_f=30×10⁻2=0.3 m.

Step 3: Calculate the displacement

Δ x

by subtracting the initial position from the final position:

Δ x = x

_f-x_i=0.3-0.1=0.2 m.

Step 4: Substitute the values of

E

and

Δ x

into the formula for potential difference:

Δ V = 1000 \cdot 0.2

Step 5: Perform the multiplication to find the potential difference. The result will be in volts (V).

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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 region around a charged particle where a force would be exerted on other charged particles. It is represented by the symbol E and is measured in volts per meter (V/m). In this case, a uniform electric field of 1000 V/m indicates that the electric force is constant throughout the specified region.

Potential Difference

Potential difference, or voltage, is the work done per unit charge in moving a charge between two points in an electric field. It is calculated as the product of the electric field strength and the distance moved in the direction of the field. The potential difference between two points can be determined using the formula V = E * d, where V is the potential difference, E is the electric field strength, and d is the distance.

Distance in Electric Field

The distance in an electric field is the linear separation between two points where the potential difference is being measured. In this scenario, the distance is calculated as the difference between the initial position (xi = 10 cm) and the final position (xf = 30 cm), which is 20 cm or 0.2 m. This distance is crucial for determining the potential difference using the electric field strength.