24. Electric Force & Field; Gauss' Law

Electric Flux

Electric Flux (part 1)

A flat sheet of paper of area 0.250 m2 is oriented so that the normal to the sheet is at an angle of 60° to a uniform electric field of magnitude 14 N/C. 
(c) For what angle φ between the normal to the sheet and the electric field is the magnitude of the flux through the sheet (i) largest and (ii) smallest? Explain your answers.

<math display="inline"><mrow><mn>1.1</mn><mo>&#x00D7;</mo><msup><mn>10</mn><mrow><mn>3</mn></mrow></msup><mo rspace="thickmathspace">&#x2062;</mo><mi mathvariant="normal" class="MathML-Unit">N</mi><mo>&#x00B7;</mo><msup><mi mathvariant="normal" class="MathML-Unit">m</mi><mn>2</mn></msup><mo>/</mo><mi mathvariant="normal" class="MathML-Unit">C</mi></mrow></math>, outward

<math display="inline"><mrow><mn>2.5</mn><mo>&#x00D7;</mo><msup><mn>10</mn><mrow><mn>3</mn></mrow></msup><mo rspace="thickmathspace">&#x2062;</mo><mi mathvariant="normal" class="MathML-Unit">N</mi><mo>&#x00B7;</mo><msup><mi mathvariant="normal" class="MathML-Unit">m</mi><mn>2</mn></msup><mo>/</mo><mi mathvariant="normal" class="MathML-Unit">C</mi></mrow></math>, outward

<math display="inline"><mrow><mn>2.5</mn><mo>&#x00D7;</mo><msup><mn>10</mn><mrow><mn>3</mn></mrow></msup><mo rspace="thickmathspace">&#x2062;</mo><mi mathvariant="normal" class="MathML-Unit">N</mi><mo>&#x00B7;</mo><msup><mi mathvariant="normal" class="MathML-Unit">m</mi><mn>2</mn></msup><mo>/</mo><mi mathvariant="normal" class="MathML-Unit">C</mi></mrow></math>, inward

<math display="inline"><mrow><mn>6.4</mn><mo>&#x00D7;</mo><msup><mn>10</mn><mrow><mn>3</mn></mrow></msup><mo rspace="thickmathspace">&#x2062;</mo><mi mathvariant="normal" class="MathML-Unit">N</mi><mo>&#x00B7;</mo><msup><mi mathvariant="normal" class="MathML-Unit">m</mi><mn>2</mn></msup><mo>/</mo><mi mathvariant="normal" class="MathML-Unit">C</mi></mrow></math>, outward

<math display="inline"><mrow><mn>6.4</mn><mo>&#x00D7;</mo><msup><mn>10</mn><mrow><mn>3</mn></mrow></msup><mo rspace="thickmathspace">&#x2062;</mo><mi mathvariant="normal" class="MathML-Unit">N</mi><mo>&#x00B7;</mo><msup><mi mathvariant="normal" class="MathML-Unit">m</mi><mn>2</mn></msup><mo>/</mo><mi mathvariant="normal" class="MathML-Unit">C</mi></mrow></math>, inward

<math display="inline"><mrow><mn>1.1</mn><mo>&#x00D7;</mo><msup><mn>10</mn><mrow><mn>3</mn></mrow></msup><mo rspace="thickmathspace">&#x2062;</mo><mi mathvariant="normal" class="MathML-Unit">N</mi><mo>&#x00B7;</mo><msup><mi mathvariant="normal" class="MathML-Unit">m</mi><mn>2</mn></msup><mo>/</mo><mi mathvariant="normal" class="MathML-Unit">C</mi></mrow></math>, inward

A cube has sides of <math display="inline"><mrow><mn>4.0</mn><mo rspace="thickmathspace">&#x2062;</mo><mi mathvariant="normal" class="MathML-Unit">cm</mi></mrow></math>. Inside the cube is a <math display="inline"><mrow><mn>20</mn><mo rspace="thickmathspace">&#x2062;</mo><mi mathvariant="normal" class="MathML-Unit">nC</mi></mrow></math> and a <math display="inline"><mrow><mo>&#x2212;</mo><mn>30</mn><mo rspace="thickmathspace">&#x2062;</mo><mi mathvariant="normal" class="MathML-Unit">nC</mi></mrow></math> charge. What is the net flux through the cube?

ELECTRIC FLUX

What is the total flux through the two surfaces depicted in the following figure? Note that surface 1 has an area of 50 cm2 and surface 2 has an area of 100 cm2 , and E = 500 N/C.<img src="https://static.studychannel.pearsonprd.tech/courses/physics/thumbnails/images/23ca185e"alt=""/>

Flux Through Cube

Flux Through Angled Surface

Magnetic and Electric Flux

Electric flux

A uniform electric field points in the positive x direction and has a magnitude of <math display="inline"><mrow><mn>40</mn><mo rspace="thickmathspace">&#x2062;</mo><mi mathvariant="normal" class="MathML-Unit">N</mi><mo>/</mo><mi mathvariant="normal" class="MathML-Unit">C</mi></mrow></math>. What is the net flux through a cube with sides <math display="inline"><mrow><mn>4.0</mn><mo rspace="thickmathspace">&#x2062;</mo><mi mathvariant="normal" class="MathML-Unit">cm</mi></mrow></math>? The cube has one corner on the origin and the positive x, y, and z axes form three of its edges.

Where does the normal vector point for a spherical shell?<img src="https://static.studychannel.pearsonprd.tech/courses/physics/thumbnails/images/9878a4be"alt=""/>

A hemispherical surface with radius r in a region of uniform electric field E→ has its axis aligned parallel to the direction of the field. Calculate the flux through the surface.<img src="https://lightcat-files.s3.amazonaws.com/problem_images/f22c7ce53316a645-1674135819709.jpg" alt="" />

Electric Flux, Gauss's Law & Electric Fields, Through a Cube, Sphere, & Disk, Physics Problems

The electric flux through each surface of a cube is given below. Which surfaces of the cube does the electric field run parallel to?&nbsp;Φ1 = 100 Nm2 /C&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;Φ4 = 0 Nm2 /C Φ2 = 20 Nm2 /C&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;Φ5 = −40 Nm2 /? Φ3 = 0 Nm2 /C&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;Φ6 = −80 Nm2 /?

Flux Through Spherical Shell due to Point Charge

A flat sheet of paper of area 0.250 m2 is oriented so that the normal to the sheet is at an angle of 60° to a uniform electric field of magnitude 14 N/C. 
(a) Find the magnitude of the electric flux through the sheet. 
(b) Does the answer to part (a) depend on the shape of the sheet? Why or why not?

A <math display="inline"><mrow><mn>4.0</mn><mo rspace="thickmathspace">&#x2062;</mo><mi mathvariant="normal" class="MathML-Unit">cm</mi><mo>&#x00D7;</mo><mn>5.0</mn><mo rspace="thickmathspace">&#x2062;</mo><mi mathvariant="normal" class="MathML-Unit">cm</mi></mrow></math> rectangle lies in the x-y plane; let the normal vector point in the z direction. What is the flux through the rectangle of a uniform electric field <math display="inline"><mrow><mover accent="true"><mi>E</mi><mo stretchy="true">&#x21C0;</mo></mover><mo>=</mo><mo stretchy="false">(</mo><mo>&#x2212;</mo><mn>7.8</mn><mo rspace="thickmathspace">&#x2062;</mo><mo>&#x00D7;</mo><mo rspace="thickmathspace">&#x2062;</mo><msup><mrow><mn>10</mn></mrow><mn>5</mn></msup><mover accent="true"><mi>j</mi><mo>&#x005E;</mo></mover><mo>+</mo><mn>2.3</mn><mo rspace="thickmathspace">&#x2062;</mo><mo>&#x00D7;</mo><mo rspace="thickmathspace">&#x2062;</mo><mn>1</mn><msup><mn>0</mn><mn>5</mn></msup><mover accent="true"><mi>k</mi><mo>&#x005E;</mo></mover><mo stretchy="false">)</mo><mi class="MathML-Unit">N</mi><mo>/</mo><mi class="MathML-Unit">C</mi></mrow></math>

A uniform electric field points in the positive x direction and has a magnitude of <math display="inline"><mrow><mn>40</mn><mo rspace="thickmathspace">&#x2062;</mo><mi mathvariant="normal" class="MathML-Unit">N</mi><mo>/</mo><mi mathvariant="normal" class="MathML-Unit">C</mi></mrow></math>. What is the total flux through a rectangle with height <math display="inline"><mrow><mn>20</mn><mo rspace="thickmathspace">&#x2062;</mo><mi mathvariant="normal" class="MathML-Unit">cm</mi></mrow></math> and width <math display="inline"><mrow><mn>45</mn><mo rspace="thickmathspace">&#x2062;</mo><mi mathvariant="normal" class="MathML-Unit">cm</mi></mrow></math>? The rectangle lies in the y-z plane.

Physics - E&M: Ch 36.1 The Electric Field Understood (2 of 17) What is Electric Flux?

Electric flux closed surface part 1

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