### Calculating Electric Flux Through the Bottom of a Car**Problem Statement:**A vertical electric field of magnitude \(2.20 \times 10^4 \, \text{N/C}\) exists above the Earth's surface on a day when a thunderstorm is brewing. A car with a rectangular size of \(6.00 \, \text{m}\) by \(3.00 \, \text{m}\) is traveling along a dry gravel roadway sloping downward at \(20.8^\circ\). Determine the electric flux through the bottom of the car. \[ \text{Electric flux} = \boxed{} \, \text{kN} \cdot \text{m}^2/\text{C} \]### Explanation:To determine the electric flux through the bottom of the car, we use the formula for electric flux:\[ \Phi_E = E \cdot A \cdot \cos(\theta)\]Where:- \( \Phi_E \) is the electric flux.- \( E \) is the electric field strength (\(2.20 \times 10^4 \, \text{N/C}\)).- \( A \) is the area through which the electric field lines pass.- \( \theta \) is the angle between the electric field and the normal (perpendicular) to the surface.### Step-by-step solution:1. **Calculate the Area (\(A\)):** The car has a rectangular bottom with dimensions \(6.00 \, \text{m}\) and \(3.00 \, \text{m}\): \[ A = 6.00 \, \text{m} \times 3.00 \, \text{m} = 18.00 \, \text{m}^2 \]2. **Determine the angle (\( \theta \)):** The electric field is vertical, and the roadway is sloping downward at \(20.8^\circ\). Since the electric field is perpendicular to the Earth's surface, the angle between the electric field and the normal to the car’s bottom is \(90^\circ - 20.8^\circ\): \[ \theta = 90^\circ - 20.8^\circ = 69.2^\circ \]3. **Calculate the Electric Flux ( \( \Phi

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A vertical electric field of magnitude 2.20 x 104 N/C exists above the Earth's surface on a day when a thunderstorm is brewing. A car with a rectangular size of 6.00 m by 3.00 m is traveling along a dry gravel roadway sloping downward at 20.8°. Determine the electric flux through the bottom of the car. kNm²/C

A vertical electric field of magnitude 2.20 x 104 N/C exists above the Earth's surface on a day when a thunderstorm is brewing. A car with a rectangular size of 6.00 m by 3.00 m is traveling along a dry gravel roadway sloping downward at 20.8°. Determine the electric flux through the bottom of the car. kNm²/C

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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