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EE2011 Lecture 3 - Electrostatics Parrt II

# 2r 2 rl therefore the potential difference between

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Unformatted text preview: between inner and outer conductors is b b Q b ln . 2 rl 2l a a a The capacitance C and capacitance C' per unit length are V E dl Q ˆ rdr 2l C ; and C ' l ln b a ln b Prof Joshua Le-Wei Li, EM Research Group Prof 24 C Q V ˆ r 2 . a EE2011: Engineering Electromagnetics Electromagnetics Electrostatic Potential Energy • Electrostatic Potential Energy – The voltage v across a capacitor C is related to charge q by v = q/C. – The work is thus dWe = vdq=qdq/C, or dW Q We q dq C 0 2 C Q /V 1Q 2C 1 CV 2 2 V Ed C A/ d 1A Ed 2d 2 12 E Ad 2 12 Ev 2 – Electrostatic energy per unit volume and energy we We v 12 E , (J/m 3 ) or We 2 1 2 E 2 dv (J). V • The half value comes from the mean square evaluation Prof Joshua Le-Wei Li, EM Research Group Prof 25 EE2011: Engineering Electromagnetics Electromagnetics Image Theory Skip slides 26 to 28 • Image Theory Prof Joshua Le-Wei Li, EM Research Group Prof 26 EE2011: Engineering Electromagnetics Electromagnetics Image Theory • Example 10 Question: Use image theory to determine V and E at an arbitrary point P(x, y, z) in the region z > 0 due to a charge Q in free space at a distance d above a grounded conducting plane. Solution: Consider a charge +Q at (0, 0, d) and its image charge –Q at (0, 0, -d) in Cartesian coordinates. Therefore, the electric field at point P(x, y, z) due to the two charges is given for z > 0 by 1 QR1 QR 2 E 3 4 0 R13 R2 ˆ ˆ ˆ xx yy z z d 1 4 0 x 2 y 2 Prof Joshua Le-Wei Li, EM Research Group Prof zd 27 2 3/ 2 ˆ ˆ ˆ xx yy z z d x 2 y 2 zd 2 3/ 2 . EE2011: Engineering Electromagnetics Electromagnetics Image Theory • Example 11 10 Prof Joshua Le-Wei Li, EM Research Group Prof 28 EE2011: Engineering Electromagnetics Electromagnetics...
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