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2. (10 points) Consider a hemisphere of radius R centred at the origin as illustrated on...
2. (5 points) Consider a hemispherical surface of radius R centred at the origin as illustrated...
2. (5 points) Consider a hemispherical surface of radius R centred at the origin as illustrated on the right. The hemisphere is contained entirely in the region 2 <0. 'T TTTT A uniform charge distribution o is placed on the hemisphere. 17 LE SITES a) Find V at the origin and at To = R2 on the 2 axis.
2.1 2.2 2 FUNDAMENTAL THEOREMS Consider the vector function u x2+ yj)+12. 2.1 15 POINTS Verify...
2.1 2.2
2 FUNDAMENTAL THEOREMS Consider the vector function u x2+ yj)+12. 2.1 15 POINTS Verify the divergence theorem for a hemisphere of radius R centred at the origin, namely x2+y+22s R2 and z20. 2.2 15 POINTS Verify the Curl theorem (Stokes' theorem) for a circle of radius R in thex-y plane centred at
(1 point) [DL:2/5] A cylindrical conductor of radius R = 0.85 m is centred on the...
(1 point) [DL:2/5] A cylindrical conductor of radius R = 0.85 m is centred on the z-axis. The current density in the conductor is given in cylindrical coordinates: J = 16e (1-p/R)a, A/m? 'a, A/m² Find the total current passing through the plane z = 0. 146.8/e
Question 6 (20 points (bonus)). On the sphere with radius R and centered at origin in...
Question 6 (20 points (bonus)). On the sphere with radius R and centered at origin in Rº consider the region D with area A. Consider the solid E constructed by the line segments from origin to the points in D. Show that the volume of Eis RA. Figure 1: Curve C
2. Spherical Dipole - The surface charge density on a sphere of radius R is constant, +0, on the entire northern hemisphere, and-oo on the entire southern hemisphere. There are no other charges prese...
2. Spherical Dipole - The surface charge density on a sphere of radius R is constant, +0, on the entire northern hemisphere, and-oo on the entire southern hemisphere. There are no other charges present inside or outside the sphere. (a) (4 pts) Compute the dipole moment of that sphere (with the +z-axis up through the pole of the positive, +Oo, hemisphere). Use the definition of a dipole moment, p-Jr, (7)dr', which in this case becomes p:-:J20(7)dA. Write your final answer...
Consider a spherical shell with inner radius a and outer radius b. A charge density σ...
Consider a spherical shell with inner radius a and outer radius b. A charge density σ A cos(9) is glued over the outer surface of the shell, while the potential at the inner surface of the shell is V (8) Vo cos(0). Find electric potential inside the spherical shell, a<r<b.
2. (10 pts.) Consider a sphere of radius R > 0 and its bounding cylinder with...
2. (10 pts.) Consider a sphere of radius R > 0 and its bounding cylinder with height 2R that is tangent to the sphere precisely in an equatorial great circle (as depicted below) Define the axial projection of the sphere onto the cylinder and show that the axial projection of the sphere onto its bounding cylinder pre- serves area. Hint: Given a point (ro, Vo, zo) on the sphere, the axial projection of the sphere onto the cylinder fixes the...
plz? help sir .......... A transparent glass hemisphere with radius R and mass m has an...
plz? help sir
..........
A transparent glass hemisphere with radius R and mass m has an index of refraction n. In the medium outside the hemisphere, the index of refraction is equal to one. A parallel beam of monochromatic laser light is incident uniformly and normally onto the central portion of its planar surface, as shown in Figure 3. The acceleration of gravity g is vertically downwards. The radius 8 of the circular cross-section of the laser beam is much...
2. Consider a circular current loop of radius R placed in the xy plane as shown in the figure. It...
The 5th page of lecture 24:
2. Consider a circular current loop of radius R placed in the xy plane as shown in the figure. It is centered at the origin and viewed down from the positive z-axis the current, lo, flows anti-clockwise. Radius = R a. In what direction does the magnetic field point at the red point in the figure, Fa? Explain clearly why this is true. current b. Since B-VxA, in which plane does Alie. Explain clearly...
2. (5 points) Consider a hemispherical surface of radius R centred at the origin as illustrated on the right. The hemisphere is contained entirely in the region 2 <0. 'T TTTT A uniform charge distribution o is placed on the hemisphere. 17 LE SITES a) Find V at the origin and at To = R2 on the 2 axis.
2.1 2.2
2 FUNDAMENTAL THEOREMS Consider the vector function u x2+ yj)+12. 2.1 15 POINTS Verify the divergence theorem for a hemisphere of radius R centred at the origin, namely x2+y+22s R2 and z20. 2.2 15 POINTS Verify the Curl theorem (Stokes' theorem) for a circle of radius R in thex-y plane centred at
(1 point) [DL:2/5] A cylindrical conductor of radius R = 0.85 m is centred on the z-axis. The current density in the conductor is given in cylindrical coordinates: J = 16e (1-p/R)a, A/m? 'a, A/m² Find the total current passing through the plane z = 0. 146.8/e
Question 6 (20 points (bonus)). On the sphere with radius R and centered at origin in Rº consider the region D with area A. Consider the solid E constructed by the line segments from origin to the points in D. Show that the volume of Eis RA. Figure 1: Curve C
2. Spherical Dipole - The surface charge density on a sphere of radius R is constant, +0, on the entire northern hemisphere, and-oo on the entire southern hemisphere. There are no other charges present inside or outside the sphere. (a) (4 pts) Compute the dipole moment of that sphere (with the +z-axis up through the pole of the positive, +Oo, hemisphere). Use the definition of a dipole moment, p-Jr, (7)dr', which in this case becomes p:-:J20(7)dA. Write your final answer...
Consider a spherical shell with inner radius a and outer radius b. A charge density σ A cos(9) is glued over the outer surface of the shell, while the potential at the inner surface of the shell is V (8) Vo cos(0). Find electric potential inside the spherical shell, a<r<b.
2. (10 pts.) Consider a sphere of radius R > 0 and its bounding cylinder with height 2R that is tangent to the sphere precisely in an equatorial great circle (as depicted below) Define the axial projection of the sphere onto the cylinder and show that the axial projection of the sphere onto its bounding cylinder pre- serves area. Hint: Given a point (ro, Vo, zo) on the sphere, the axial projection of the sphere onto the cylinder fixes the...
plz? help sir
..........
A transparent glass hemisphere with radius R and mass m has an index of refraction n. In the medium outside the hemisphere, the index of refraction is equal to one. A parallel beam of monochromatic laser light is incident uniformly and normally onto the central portion of its planar surface, as shown in Figure 3. The acceleration of gravity g is vertically downwards. The radius 8 of the circular cross-section of the laser beam is much...
The 5th page of lecture 24:
2. Consider a circular current loop of radius R placed in the xy plane as shown in the figure. It is centered at the origin and viewed down from the positive z-axis the current, lo, flows anti-clockwise. Radius = R a. In what direction does the magnetic field point at the red point in the figure, Fa? Explain clearly why this is true. current b. Since B-VxA, in which plane does Alie. Explain clearly...
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