## Part A**Question:**What is the diameter of the smaller sphere?**Answer Input:**\( D_{\text{small}} = \) [Input box] cm- **Buttons and Tools:** - A button for mathematical equation editor. - A button for Greek letters and symbols. - Undo and redo arrows. - Refresh symbol to clear input. - A keyboard icon.- **Action:** - A "Submit" button for submitting the answer. - A "Request Answer" link for assistance.## Part B**Question:**What is the diameter of the larger sphere?**Answer Input:**\( D_{\text{large}} = \) [Input box] cm- **Buttons and Tools:** - A button for mathematical equation editor. - A button for Greek letters and symbols. - Undo and redo arrows. - Refresh symbol to clear input. - A keyboard icon.- **Action:** - A "Submit" button for submitting the answer. **Title: Understanding Spherical Capacitors****Introduction:**A spherical capacitor is a type of capacitor that consists of two concentric spherical conducting shells. It is used to store electrical energy in the form of an electric field between the two shells.**Description:**The image illustrates a spherical capacitor with the following components:- **Inner Radius (\( r_{\text{in}} \)):** This is the radius of the inner spherical shell. - **Outer Radius (\( r_{\text{out}} \)):** This is the radius of the outer spherical shell.- **Gap:** The space between the inner and outer shells. In this example, the gap is specified as 1.70 mm.**Key Information:**- The spherical capacitor has a capacitance of 50.0 pF (picofarads).**Diagram Explanation:**The diagram shows two concentric circles representing the cross-section of the inner and outer spherical shells. A double-headed arrow labeled "gap" indicates the distance between these two shells.**Conclusion:**Spherical capacitors are crucial in various applications due to their ability to store charge. The capacitance depends on the radii of the spheres and the dielectric material filling the gap between them. Understanding the configuration and spacing of the spherical shells is vital for calculating the capacitance accurately.

(a) The expression for the capacitance of a spherical capacitor is as follows; C=4πε01rin-1rout 1 The expression for outer radius can be written as rout=rin+r0 2 Use equation (2) in (1) to find the inner radius of the capacitor. C=4πε01rin-1rin+r01rin-1rin+r0=4πε0Crin+r0-rinrin+r0rin=4πε0C0=rin24πε0C+r04πε0Crin-r0 3Substitute the values in (3) to find the inner radius of the capacitor (ignore the units). 0=rin24π8.854×10-1250.0×10-12+1.70×10-34π8.854×10-1250.0×10-12-1.70×10-30=2.225rin2+3.78×10-3rin-1.70×10-3rin=-3.78×10-3±3.78×10-32+42.2251.70×10-322.225rin=0.0268 m 4 The diameter of the smaller spher is as follows: Dsmall=2rinDsmall=20.0268 mDsmall=0.0536 mDsmall=5.36 cm 5 (b) The radius of the outer sphere is as follows: rout=0.0268 m+1.70×10-3mrout=0.0285 m 6 The diameter of the larger sphere is as follows: Dlarger=2routDlarger=20.0285 mDlarger=0.057 mDlarger=5.7 cm 7

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What is the diameter of the smaller sphere? ΑΣφ Dsmall = Submit Request Answer • Part B What is the diameter of the larger sphere?