Suppose F is a radial force field, S1 is a sphere of radius 4 centered at the origin, and the...
Let S2 be a sphere of radius 12 centered at the origin, and consider the flux integral ??S2 F ·dS.
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Suppose F is a radial force field, S1 is a sphere of radius 4 centered at the origin, and the...
r 37. Singular radial field Consider the radial field (x, y, z) F (x2 + y2...
r 37. Singular radial field Consider the radial field (x, y, z) F (x2 + y2 + z2)1/2" a. Evaluate a surface integral to show that SsFonds = 4ta?, where S is the surface of a sphere of radius a centered at the origin. b. Note that the first partial derivatives of the components of F are undefined at the origin, so the Divergence Theorem does not apply directly. Nevertheless, the flux across the sphere as computed in part (a)...
Let V be the solid sphere of radius a centred at the origin. Let S be...
Let V be the solid sphere of radius a centred at the origin. Let S be the surface of V oriented with outward unit normal. Consider the vector field F(x, y, z) (xi + yj + zk) (x2 + y2 + z2)3/2 (a) Evaluate the flux integral Sle F:ñ ds by direct calculation. (b) Evaluate SIL, VF DV by direct calculation. (c) Compare your answers to parts (a) and (b) and explain why Gauss' theorem does not apply.
A sphere of radius R is centered at the origin. A constant magnetic field of magnitude...
A sphere of radius R is centered at the origin. A constant magnetic field of magnitude B is in the +k direction. What is the value of the magnetic flux that passes through the hemispherical surface that has z<0? (This is the half of the surface of the sphere in the region z<0.) Define the flux to be positive if it points from the inside of the sphere to the outside. a) 2 B b) -2B c) - TPB d)...
2. Consider the circle of radius 9 centered at the origin in the ry-plane. It can be described by the equation 2 +y2 81. The sphere of radius 9 centered at the origin can be created by rotating the c...
2. Consider the circle of radius 9 centered at the origin in the ry-plane. It can be described by the equation 2 +y2 81. The sphere of radius 9 centered at the origin can be created by rotating the curve y v81- about the a-axis. (a) The volume of the sphere can be calulated using a definite integral. Set up that definite integral, but do not solve it. (b) Complete the calculation of the integral.
2. Consider the circle of...
12. -1 points My Notes Suppose G is a vector field with the property that divG = 3 for 2 21Tt Fin...
12. -1 points My Notes Suppose G is a vector field with the property that divG = 3 for 2 21Tt Find the flux of G through the sphere of radius 8 centered at the origin Il ril 10 and that the flux of G through the sphere of radius 4 centered at the origin is flux :
12. -1 points My Notes Suppose G is a vector field with the property that divG = 3 for 2 21Tt Find...
Divergence Theorem: Problem 4 Previous Problem Problem List Next Problenm (1 point) Evaluate JM F dS where F (3ay2,3a^y, z3) and M is the surface of the sphere of radius 2 centered at the origin....
Divergence Theorem: Problem 4 Previous Problem Problem List Next Problenm (1 point) Evaluate JM F dS where F (3ay2,3a^y, z3) and M is the surface of the sphere of radius 2 centered at the origin.
Divergence Theorem: Problem 4 Previous Problem Problem List Next Problenm (1 point) Evaluate JM F dS where F (3ay2,3a^y, z3) and M is the surface of the sphere of radius 2 centered at the origin.
3) A Gaussian sphere of radius r is centered at the origin. A point charge q...
3) A Gaussian sphere of radius r is centered at the origin. A point charge q is within the sphere, but not at the origin. The electric flux through the sphere equals (A) zero (O)méai (D) mCra
GIVEN: Ω isthe portion of the surface of the sphere centered at the origin of radius 3 above 1.2 1(xy, z) the plane, z-2: Ω: the field F = (x, x,x). a) FIND the flux of VrF through Ω in the given...
GIVEN: Ω isthe portion of the surface of the sphere centered at the origin of radius 3 above 1.2 1(xy, z) the plane, z-2: Ω: the field F = (x, x,x). a) FIND the flux of VrF through Ω in the given direction: n has positive 2-component. HINT: (radius a)on Q:(spherical coordinates) b) Parameterize the path,c-a2, (r,g,z)asin g dode with orientation to agree with the given n for Ω ANS: (a) 5 c) With positive orientation,an -e DETERMINE: F.ds ANS:...
A conducting sphere with radius R is centered at the origin. The sphere is grounded having...
A conducting sphere with radius R is centered at the origin. The sphere is grounded having an electric potential of zero. A point charge Q is brought toward the sphere along the z- axis and is placed at the point ะ-8. As the point charge approaches the sphere mobile charge is drawn from the ground into the sphere. This induced charge arranges itself over the surface of the sphere, not in a uniform way, but rather in such a way...
3. If S is a sphere, and F is a vector field that fulfills the hypotheses of Stokes' Theorem, then what is the value of curl F dS? (d) It cannot be determined without knowing F. (e) None of the o...
3. If S is a sphere, and F is a vector field that fulfills the hypotheses of Stokes' Theorem, then what is the value of curl F dS? (d) It cannot be determined without knowing F. (e) None of the other choices 4. True or False? Suppose that Si and S2 are oriented piecewise-smooth surfaces that share the same simple, closed, piecewise-smooth boundary curve C. Let F be a vector field whose components have continuous partial derivatives on an open...
r 37. Singular radial field Consider the radial field (x, y, z) F (x2 + y2 + z2)1/2" a. Evaluate a surface integral to show that SsFonds = 4ta?, where S is the surface of a sphere of radius a centered at the origin. b. Note that the first partial derivatives of the components of F are undefined at the origin, so the Divergence Theorem does not apply directly. Nevertheless, the flux across the sphere as computed in part (a)...
Let V be the solid sphere of radius a centred at the origin. Let S be the surface of V oriented with outward unit normal. Consider the vector field F(x, y, z) (xi + yj + zk) (x2 + y2 + z2)3/2 (a) Evaluate the flux integral Sle F:ñ ds by direct calculation. (b) Evaluate SIL, VF DV by direct calculation. (c) Compare your answers to parts (a) and (b) and explain why Gauss' theorem does not apply.
A sphere of radius R is centered at the origin. A constant magnetic field of magnitude B is in the +k direction. What is the value of the magnetic flux that passes through the hemispherical surface that has z<0? (This is the half of the surface of the sphere in the region z<0.) Define the flux to be positive if it points from the inside of the sphere to the outside. a) 2 B b) -2B c) - TPB d)...
2. Consider the circle of radius 9 centered at the origin in the ry-plane. It can be described by the equation 2 +y2 81. The sphere of radius 9 centered at the origin can be created by rotating the curve y v81- about the a-axis. (a) The volume of the sphere can be calulated using a definite integral. Set up that definite integral, but do not solve it. (b) Complete the calculation of the integral.
2. Consider the circle of...
12. -1 points My Notes Suppose G is a vector field with the property that divG = 3 for 2 21Tt Find the flux of G through the sphere of radius 8 centered at the origin Il ril 10 and that the flux of G through the sphere of radius 4 centered at the origin is flux :
12. -1 points My Notes Suppose G is a vector field with the property that divG = 3 for 2 21Tt Find...
Divergence Theorem: Problem 4 Previous Problem Problem List Next Problenm (1 point) Evaluate JM F dS where F (3ay2,3a^y, z3) and M is the surface of the sphere of radius 2 centered at the origin.
Divergence Theorem: Problem 4 Previous Problem Problem List Next Problenm (1 point) Evaluate JM F dS where F (3ay2,3a^y, z3) and M is the surface of the sphere of radius 2 centered at the origin.
3) A Gaussian sphere of radius r is centered at the origin. A point charge q is within the sphere, but not at the origin. The electric flux through the sphere equals (A) zero (O)méai (D) mCra
GIVEN: Ω isthe portion of the surface of the sphere centered at the origin of radius 3 above 1.2 1(xy, z) the plane, z-2: Ω: the field F = (x, x,x). a) FIND the flux of VrF through Ω in the given direction: n has positive 2-component. HINT: (radius a)on Q:(spherical coordinates) b) Parameterize the path,c-a2, (r,g,z)asin g dode with orientation to agree with the given n for Ω ANS: (a) 5 c) With positive orientation,an -e DETERMINE: F.ds ANS:...
A conducting sphere with radius R is centered at the origin. The sphere is grounded having an electric potential of zero. A point charge Q is brought toward the sphere along the z- axis and is placed at the point ะ-8. As the point charge approaches the sphere mobile charge is drawn from the ground into the sphere. This induced charge arranges itself over the surface of the sphere, not in a uniform way, but rather in such a way...
3. If S is a sphere, and F is a vector field that fulfills the hypotheses of Stokes' Theorem, then what is the value of curl F dS? (d) It cannot be determined without knowing F. (e) None of the other choices 4. True or False? Suppose that Si and S2 are oriented piecewise-smooth surfaces that share the same simple, closed, piecewise-smooth boundary curve C. Let F be a vector field whose components have continuous partial derivatives on an open...
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