Explanation Given data: The radius of the infinitely long cylinder is a . The distance from the parallel conducting plate is d . Calculation: The required diagram is shown in Figure 1 and Figure 2. Let assume that the cylinder in Figure 1 have the charge density ρ l at the distance d . So, the image of the cylinder in Figure 2 have the charge density − ρ l at the distance − d . The electric field at a distance ( d − z ) from the center of real the cylinder is given by, E 1 = − z ^ ρ l 2 π ε 0 ( d − z ) Here, ε 0 is the permittivity of the air which has the standard value as ( 8.85 × 10 − 12 F / m ) . The electric field at a distance ( d + z ) from the center of the image cylinder is given by, E 2 = z ^ ( − ρ l ) 2 π ε 0 ( d + z ) The potential difference V from the initial point z 1 = − ( d − a ) to the final point z 2 = ( d − a ) is given as, V = − ∫ − ( d − a ) ( d − a ) ( E 1 + E 2 ) ⋅ z ^ d z Substitute − z ^ ρ l 2 π ε 0 ( d − z ) for E 1 and z ^ ( − ρ l ) 2 π ε 0 ( d + z ) for E 2 in the above equation

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ISBN: 8220100663659

Author: ULABY

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Chapter 4, Problem 63P

To determine

The capacitance per unit length for the given condition.

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Chapter 4, Problem 62P

Chapter 5.1, Problem 1CQ

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Chapter 4 Solutions

EBK FUNDAMENTALS OF APPLIED ELECTROMAGN

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The capacitance per unit length for the given condition.

Solution Summary: The required diagram is shown in Figure 1 and Figure 2. The electric field at a distance (d-z) from the center of the image cylinder is given by,

The capacitance per unit length for the given condition.

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Chapter 4 Solutions