A capacitor consists of two concentric spherical shells (inner radius a and outer radius b). The inner shell is at a potential of Vo and the outer shell is grounded. The dielectric between the two shells has the permittivity of E. a) Using Laplace's equation, determine the potential distribution in the space between two shells.
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- A parallel-plate capacitor with plates of area LW and plate separation t has the region between its plates filled with wedges of two dielectric materials as shown. Assume t is much less than both L and W. (a) Determine its capacitance. (b) Should the capacitance be the same if the labels k1 and k2 are interchanged? Demonstrate that your expression does or does not have this property. (c) Show that if k1 and k2 approach equality to a common value k, your result becomes the same as the capacitance of a capacitor containing a single dielectric: C = k∈0LW/t.A capacitor is constructed out of two circular plates, each of radius 6 cm. The plates are separated by 6.6 mm. The space between the plates is filled with a dielectric of relative permittivity 1.3. Calculate the capacitance, neglecting edge effects, in units of 10-12 F (that is, picofarads). Use that the permittivity of free space is 8.85 x 10-12 F/m. (Please answer to the fourth decimal place - i.e 14.3225)A capacitor is formed from two concentric spherical conducting shells separated by vacuum. The inner sphere has radius 11.5 cm, and the outer sphere has radius 15.5 cm. A potential difference of 120.0 V is applied to the capacitor. a) What is the energy density at r = 11.6 cm, just outside the inner sphere? b) What is the energy density at r = 15.4 cm, just inside the outer sphere?
- A spherical capacitor contains a charge of 3.00 nC when connected to a potential difference of 230.0 V. Its plates are separated by vacuum and the inner radius of the outer shell is 4.30 cm. Calculate the capacitance.If the magnitude of the electric field in air exceeds roughly 3 x 106 N/C, the air breaks down and a spark forms. For a two-disk capacitor of radius 26 cm with a gap of 1 mm, what is the maximum charge (plus and minus) that can be placed on the disks without a spark forming (which would permit charge to flow from one disk to the other)? i CA certain substance has a dielectric constant of 3.8 and a dielectric strength of 25 MV/m. If it is used as the dielectric material in a parallel-plate capacitor, what minimum area should the plates of the capacitor have to obtain a capacitance of 5.3 × 10-2 µ F and to ensure that the capacitor will be able to withstand a potential difference of 3.1 kV?
- An air-filled spherical capacitor is constructed with an inner-shell radius of 7.40 cm and an outer-shell radius of 15.8 cm. (a) Calculate the capacitance of the device. (b) What potential difference between the spheres results in a 4.00 µC charge on the capacitor? (c) What If? What would be the length (in cm) of a cylindrical air-filled capacitor with the same inner and outer radii as the spherical capacitor if it were to have the same capacitance as the spherical capacitor?An air-filled spherical capacitor is constructed with an inner-shell radius of 7.45 cm and an outer-shell radius of 13.5 cm. (a) Calculate the capacitance of the device.(b) What potential difference between the spheres results in a 4.00-µC charge on the capacitor?A 7.44 µF isolated capacitor is constructed with Teflon, having a dielectric constant of 2.10, between the plates. The capacitor is initially charged to 1.34 volts, and then the Teflon is removed. After removing the Teflon, what is the potential difference across the capacitor plates?
- Two parallel plates having equal and opposite charges with area L x L separation d is filled with a dielectric material as shown in the Figure. The related dielectric constant varies with zask=a+ Here, a 46 cm, b -92 cm, d 0.31 cm and L=1m are given. Find the capacitance of this capacitor in 10-11 Farad. Take o=10-¹¹ C²/Nm². Answer:An air-filled spherical capacitor is constructed with an inner-shell radius of 7.40 cm and an outer-shell radius of 13.0 cm. (a) Calculate the capacitance of the device. (b) What potential difference between the spheres results in a 4.00 µC charge on the capacitor? (c) What If? What would be the length (in cm) of a cylindrical air-filled capacitor with the same inner and outer radii as the spherical capacitor if it were to have the same capacitance as the spherical capacitor?Please don't provide handwritten solution .....