Vernier Software & Technology

# Electric Field Due to a Line of Charge

## Introduction

Consider a thin insulated rod that carries a known negative charge Qrod that is uniformly distributed. It is possible to determine the electric field along a line perpendicular to the rod that passes through its center using the following equation – often derived in introductory texts:

$\vec E_{{\text{rod}}}^{{\text{theory}}} = \frac{{\left( {k{Q_{{\text{rod}}}}} \right)}} {{r\sqrt {{r^2} + {{(L/2)}^2}} }}\hat i$

where L is the length of the charged part of the rod, r is the distance from the test charge to the center of the charged part of the rod, and Qrod is its total charge. The constant k is the well-known Coulomb constant.

## Objectives

In this activity, you will

• Examine a digital movie of a charged rod exerting a force on a hanging “test charge” along with a Logger Pro analysis to determine if the theoretical equation describes the relationship between r, L and the measured electric field, $\vec E_{{\text{rod}}}^{{\text{meas}}}$ at the location of the test charge.

## Software for Experiment

This experiment uses Logger Pro software for video analysis. The video for analysis is included with the lab book.

## Physics with Video Analysis

See other experiments from the lab book.

 1 Rolling Ball 2 Big and Small: How to Scale an Image 3 Velocity Change 4 Velocity and Speed 5 Velocity and Acceleration 6 Three Movies: Determining Constant Acceleration 7 Demon Drop: A Mathematical Modeling Activity 8 Jumping on the Moon 9 2D Vectors: Pool Ball Displacement, Velocity, and Speed 10 Galileo's Projectile I: Using 17th Century Techniques 11 Galileo's Projectile II: Using Contemporary Techniques 12 Projectile Motion Vectors 13 Frictional Slowing 14 Impulsive Juggling 15 Center of Mass Motions 16 Finding a Spring Constant 17 Net Work - Kinetic Energy Theorem 18 Oscillations 19 Slinky Wave Speeds 20 Superposition of Slinky Waves 21 A Wave Pulse Equation 22 Doppler Effect: Surface Water Waves 23 Doppler Effect: Sound Waves 24 A Heat Engine: Relating Work to the P-V Cycle 25 Coulomb's Law for Two Charged Spheres 26 Discharge Rate 27 Electric Field Due to a Line of Charge 28 Resistance and Ohm's Law 29 Parallel Plate Capacitor: Potential Difference vs. Spacing 30 Wiring Capacitors in Series and Parallel 31 Using RC Decay to Determine Capacitance 32 Exploring Faraday's Law 33 Snell's Law of Refraction

### Experiment 27 from Physics with Video Analysis Lab Book

#### Included in the Lab Book

Vernier lab books include word-processing files of the student instructions, essential teacher information, suggested answers, sample data and graphs, and more.