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Question 6 (20 points (bonus)). On the sphere with radius R and centered at origin in...
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)...
Tangent plane to a sphere: Consider the sphere of radius R centered on the origin in...
Tangent plane to a sphere: Consider the sphere of radius R centered on the origin in 3 dimensions. Now consider the point o = Doi+yoj + zok. Write the equations for any two (non-parallel) planes which pass through both the point to and the origin. Using these planes, write the equation for the tangent plane of the sphere at the point to. (Hint: think about how the tangent plane of a sphere must be perpendicular to a line connecting the...
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...
6. Let E be the region of R3 inside the intersection of the sphere centered on...
6. Let E be the region of R3 inside the intersection of the sphere centered on the origin of radius 2 and of the sphere of radius 2 centered on the point (0,0,2). (a) Write a triple iterated integral representing the volume of the region E. Do not evaluate it! 5 marks (b) Show that the volume of the region E is smaller than 6tT, without evaluating any integral [4 marks
6. Let E be the region of R3 inside...
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
Question: A sphere of radius 1m is centered at the origin and has a density that...
Question: A sphere of radius 1m is centered at the origin and has a density that varies with distance outward from the origin as p(r) = 2000 kg exp(- ). (r is the distance to a particular point within the sphere from the origin, and this says that the density is 2000 kg in the center and about 736 kg at the surface) What is the total mass of the sphere? Hint: you'll obviously have to set-up and do an...
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 SOLID SPHERE Consider a solid sphere of radius R with charge per unit volume that...
3 SOLID SPHERE Consider a solid sphere of radius R with charge per unit volume that depends only on the distance from the origin, r, 3.1 15 POINTS Compute the electric field everywhere inside the sphere. direction of E as a function of position within the sphere. Be sure to state the magnitude and 3.2 10 POINTS Compute the electric field everywhere outside the sphere.
3 SOLID SPHERE Consider a solid sphere of radius R with charge per unit volume that...
3 SOLID SPHERE Consider a solid sphere of radius R with charge per unit volume that depends only on the distance from the origin, r, 3.1 15 POINTS Compute the electric field everywhere inside the sphere. Be sure to state the magnitude and direction of E as a function of position within the sphere. 3.2 10 POINTS Compute the electric field everywhere outside the sphere.
Summary 583 Bridging Problem An imaginary sphere of radius R is centered at the origin, as...
Summary 583 Bridging Problem An imaginary sphere of radius R is centered at the origin, as shown in Pigure 17,37. A charge q is rigidly fixed to the x axis at +R/2 and a second charge g is at-R2. Finally, a proton (of mass and charge te) is released from rest oa the y axis. in terms of e, m, R of the proton at the moment it is released from y +R/4. (b) What are the magnitude and direction...
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)...
Tangent plane to a sphere: Consider the sphere of radius R centered on the origin in 3 dimensions. Now consider the point o = Doi+yoj + zok. Write the equations for any two (non-parallel) planes which pass through both the point to and the origin. Using these planes, write the equation for the tangent plane of the sphere at the point to. (Hint: think about how the tangent plane of a sphere must be perpendicular to a line connecting the...
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...
6. Let E be the region of R3 inside the intersection of the sphere centered on the origin of radius 2 and of the sphere of radius 2 centered on the point (0,0,2). (a) Write a triple iterated integral representing the volume of the region E. Do not evaluate it! 5 marks (b) Show that the volume of the region E is smaller than 6tT, without evaluating any integral [4 marks
6. Let E be the region of R3 inside...
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
Question: A sphere of radius 1m is centered at the origin and has a density that varies with distance outward from the origin as p(r) = 2000 kg exp(- ). (r is the distance to a particular point within the sphere from the origin, and this says that the density is 2000 kg in the center and about 736 kg at the surface) What is the total mass of the sphere? Hint: you'll obviously have to set-up and do an...
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 SOLID SPHERE Consider a solid sphere of radius R with charge per unit volume that depends only on the distance from the origin, r, 3.1 15 POINTS Compute the electric field everywhere inside the sphere. direction of E as a function of position within the sphere. Be sure to state the magnitude and 3.2 10 POINTS Compute the electric field everywhere outside the sphere.
3 SOLID SPHERE Consider a solid sphere of radius R with charge per unit volume that depends only on the distance from the origin, r, 3.1 15 POINTS Compute the electric field everywhere inside the sphere. Be sure to state the magnitude and direction of E as a function of position within the sphere. 3.2 10 POINTS Compute the electric field everywhere outside the sphere.
Summary 583 Bridging Problem An imaginary sphere of radius R is centered at the origin, as shown in Pigure 17,37. A charge q is rigidly fixed to the x axis at +R/2 and a second charge g is at-R2. Finally, a proton (of mass and charge te) is released from rest oa the y axis. in terms of e, m, R of the proton at the moment it is released from y +R/4. (b) What are the magnitude and direction...
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