2. (5 points) Consider a hemispherical surface of radius R centred at the origin as illustrated...
2. (10 points) Consider a hemisphere of radius R centred at the origin as illustrated on the right. The hemisphere is contained entirely in the region z < 0 ion σ is placed on the hemisphere. ut a) Find E at the origin and atRê on the axis. b) Find V at the origin and at rp-RE on the z axis.
Flex question A hemispherical close surface of radius R is placed in a uniform field of magni- tude E. i)What would be the flux through the entire closed surface? ii)What is the flux through the dome of the hemisphere? Select one: a. i), ii) ERR b. i), ii) c. i)2ER2, ii) d. i)ETR, ii) e. i)-ErR2, ii)0 f. i)2E+R2, ii)ErR g. 100, ii)-ETR2 Next
Problem 2 A hemispherical surface with radius R is a region of uniform electric field E has its axis aligned parallel to the direction of the field. Derive an expression for the electric flux through the surface. Final answer not given
2. Hemispherical Bowl An inverted hemispherical bowl of radius R carries a uniform surface charge density σ. Find the potential difference between the "north" pole and the center.
Problem 1: Dipole moment. We have a sphere of radius R with a uniform surface charge density +ao over the northern hemisphere, and -oo over the southern hemisphere (oo is a positive constant). There are no other charges present inside or outside the sphere. Compute the dipole moment p of this charge distribution assuming the z-axis is the symmetry axis of the distribution. Does p depend on your choice of origin? Why or why not? Are any components of p...
1. (5 points) A semi-annulus with inner radius rı and outer radius r2 is placed on the ry plane at z 0, with centre of the radii at the origin, sllustrated. The half-annulus has a uniform surface charge density ơ r 2 a) Find the potential V at the origin. b) Find E at the origin. (Can you use the result of a) to get E?)
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
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...
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.
Problem 2: Show whether the Stoke's theorem is valid for the following function while uniformly distributed charge is contained within a surface with radius R, centered at the origin within xy plane:
Problem 2: Show whether the Stoke's theorem is valid for the following function while uniformly distributed charge is contained within a surface with radius R, centered at the origin within xy plane: