5. a. Use the Laplace equation to determine the expression for the electric potential in the...
5.
a. Use the Laplace equation to determine the expression for the electric potential in the region between two concentric metal shells (spherical capacitor) of radii a and b (a Vo, and the outer shell is grounded. [the solution to the Laplace equation is spherical coordinates has the form V = -K1/r + K2]
b. From your answer in a), determine E⃗ .
c. From your answer in b), determine the surface charge density and the total charge on the surface at r = a.
d. What is the capacitance of this spherical capacitor?
Homework Answers
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5.
a. Use the Laplace equation to determine the expression for the
electric potential in the...
Please Justify Answers and Show All work. 3. Two concentric spherical metal shells have radii a...
Please Justify Answers and
Show All work.
3. Two concentric spherical metal shells have radii a and 2a as shown in the figure on the right. The outer shell has a charge Q, but the inner shell is grounded. This means that the inner shell is at zero potential. While its potential is zero, the inner shell is not electrically neutral. The outer shell induces a charge lin on the inner shell. (The charges are taken from ground). Answer the...
electromagnetic fields theory B: ANSWER ONLY ONE (1) QUESTION ON 5 120 MARKS gure 3 shows a spherical type capacitor...
electromagnetic fields theory
B: ANSWER ONLY ONE (1) QUESTION ON 5 120 MARKS gure 3 shows a spherical type capacitor used to measure the volume of liquids, consists of wo spherical shells where the inner and outer radii given by a and b, respectively are Find the electric field E in the region a <r<bif the total charge on the surface ra is given by O 15 Marks C81, PO, 62 (ii) Express the potential difference V between r Derive...
The space between two concentric conducting spherical shells of radii b = 1.70 cm and a...
The space between two concentric conducting spherical shells of radii b = 1.70 cm and a = 1.20 cm is filled with a substance of dielectric constant κ = 20.5. A potential difference V = 62.0 V is applied across the inner and outer shells. (a) Determine the capacitance of the device. (b) Determine the free charge q on the inner shell. (c) Determine the charge q' induced along the surface of the inner shell.
The space between two concentric conducting spherical shells of radii b = 2.20 cm and a...
The space between two concentric conducting spherical shells of radii b = 2.20 cm and a = 1.20 cm is filled with a substance of dielectric constant κ = 24.2. A potential difference V = 50.0 V is applied across the inner and outer shells. Determine (a) the capacitance of the device, (b) the free charge q on the inner shell, and (c) the charge q induced along the surface of the inner shell.
Two concentric spherical shells of diameter 13.6 cm and 29.0 cm are used to form a...
Two concentric spherical shells of diameter 13.6 cm and 29.0 cm are used to form a spherical capacitor. The charges on the inner and outer shells are −9.00 µC and +9.00 µC, respectively. (a) Determine the potential difference from the inner to the outer shell. Use the fact that the magnitude of the electric field at a distance r from the center of the inner shell is given by E = KQ/r2, where K is Coulomb's constant and Q is...
A small conducting spherical shell with inner radius a and outer radius b is concentric with a larger conducting spherical shell with inner radius c and outer radius d.
A small conducting spherical shell with inner radius a and outer radius b is concentric with a larger conducting spherical shell with inner radius c and outer radius d. The inner shell has total charge +2q, and the outer shell has charge +4q. (a) Calculate the magnitude of the electric field in terms of q and the distance r from the common center of the two shells for r < a, b < r < c, and r > d. Note...
A conducting sphere of radius a, at potential Vo, is surrounded by a thin concentric spherical...
A conducting sphere of radius a, at potential Vo, is surrounded by a thin concentric spherical shell of radius b, over which someone has glued a surface charge density σ(8)-k cos θ, where k is a constant and θ is the polar spherical coordinate. (a) Find the potential in each region: (i)r > b, and () a<r<b. [5 points] [Hint: start from the general solution of Laplace's equation in spherical coordinates, but allow for different coefficients in the radial part...
A point charge is located at the center of a thin spherical conducting shell of inner...
A point charge is located at the center of a thin spherical conducting shell of inner and outer radii r and r2, respectively. A second thin spherical conducting shell of inner and outer radiR1 and R2. respectively, is concentric with the first shell. The flux is as follows for the different regions of this arrangement. Φ 10.1 103 N·m2/C for r < r o for 2 Ф-38.7 x 103 N-m2/C forpsrcR1 Φ_Ofor R1 < r < R2 p -38.7 x...
3. Select the correct sketch of the direction of dipole moment of pair of charges a)...
3. Select the correct sketch of the direction of dipole moment of pair of charges a) e b) 19 c) d) Consider two concentric conducting spherical shells. In the figure, the inner shell has an inner radius of a and an outer radius of b, and the outer shell has an inner radius of c and an outer radius of d. Inner shell carries an excess charge of-1q and outer shell carries 4. (4.1) The charge on the inner surface...
Two concentric spherical shells of diameter 13.6 cm and 26.0 cm are used to form a...
Two concentric spherical shells of diameter 13.6 cm and 26.0 cm are used to form a spherical capacitor. The charges on the inner and outer shells are −5.00 µC and +5.00 µC, respectively. (a) Determine the potential difference from the inner to the outer shell. Use the fact that the magnitude of the electric field at a distance r from the center of the inner shell is given by E = kQ/ r2 , where k is Coulomb's constant and...
Please Justify Answers and
Show All work.
3. Two concentric spherical metal shells have radii a and 2a as shown in the figure on the right. The outer shell has a charge Q, but the inner shell is grounded. This means that the inner shell is at zero potential. While its potential is zero, the inner shell is not electrically neutral. The outer shell induces a charge lin on the inner shell. (The charges are taken from ground). Answer the...
electromagnetic fields theory
B: ANSWER ONLY ONE (1) QUESTION ON 5 120 MARKS gure 3 shows a spherical type capacitor used to measure the volume of liquids, consists of wo spherical shells where the inner and outer radii given by a and b, respectively are Find the electric field E in the region a <r<bif the total charge on the surface ra is given by O 15 Marks C81, PO, 62 (ii) Express the potential difference V between r Derive...
A conducting sphere of radius a, at potential Vo, is surrounded by a thin concentric spherical shell of radius b, over which someone has glued a surface charge density σ(8)-k cos θ, where k is a constant and θ is the polar spherical coordinate. (a) Find the potential in each region: (i)r > b, and () a<r<b. [5 points] [Hint: start from the general solution of Laplace's equation in spherical coordinates, but allow for different coefficients in the radial part...
A point charge is located at the center of a thin spherical conducting shell of inner and outer radii r and r2, respectively. A second thin spherical conducting shell of inner and outer radiR1 and R2. respectively, is concentric with the first shell. The flux is as follows for the different regions of this arrangement. Φ 10.1 103 N·m2/C for r < r o for 2 Ф-38.7 x 103 N-m2/C forpsrcR1 Φ_Ofor R1 < r < R2 p -38.7 x...
3. Select the correct sketch of the direction of dipole moment of pair of charges a) e b) 19 c) d) Consider two concentric conducting spherical shells. In the figure, the inner shell has an inner radius of a and an outer radius of b, and the outer shell has an inner radius of c and an outer radius of d. Inner shell carries an excess charge of-1q and outer shell carries 4. (4.1) The charge on the inner surface...
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