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wileyPLUS: Myw eyPLUS 1 Help 1 Contact Us 1 Log Out US GENERAL ANALYTICAL PHYSICS (PHYS 211 & 212) Halliday, Fundamentals of Physics, 10e Gradebook ORION Downloadable eTextbook FULL SCREEN PRINTER VERSIONBACK NEXT Chapter 23, Problem 002 An electric field given by E-8.6-3.+2.9) pierces the Gasussian cube of edge length 0.680 m and positioned as shown in the figure. (The magnitude E is in newtons per coulomb and the position x is in meters.) What is the electric flux through the (a) top face, (b) bottom face, (e) left face, and (d) back face? (e) What is the net electric flux through the cube? Gaussian surface (a) Number (b) Number (c) Number (d) Number (e) Number obisx i 2000-2018,2shnnityasonunG Ad Rights Reserved. A Division of 2ennyiexssosis. MacBook Air 2 3 4 5 6

Explanation / Answer

We have

E = 8.6*i - 3.6(y2 + 2.9)j N/C

According to figure given in the question

Bottom face is on x-z plane

Therefore, for bottom face of cube

y = 0

And for top face

y = 6

Therefore

E along y- axis at bottom face = 8.6*i - 3.6*2.9*j N/C

And E along y - axis at top face = 8.6*i - 3.6(0.68*0.68+2.9)j N/C = 8.6*i - 12.105*j N/C

Therefore, electric flux through top surface = y-component of E * area of top surface = -12.105 * (0.68*0.68) = -5.6 N-m2/C

Flux is negative because of normal to surface and electric field are in opposite direction

E at bottom of cube = y- component of E at bottom * area of cube = -10.44 * (-0.68*0.68) = 4.827 N-m2/C

E at left side of cube = x- component of E at left side * area of side of cube = 8.6*(-0.68*0.68) = -3.97 N-m2/C

Electric flux at back face of cube = z-component of E * area of side of cube = 0

Total electric flux through cube = electric flux through top surface + flux through bottom surface + flux through left side + flux through right surface+ flux through front surface + flux through back surface = -5.6 + 4.827 + (-3.97) + 3.97 + 0+0 = 0.773 N-m2/C. ANSWER

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