10:14.pdf

# 10:14.pdf - Electric Potential Lecture 8 Electric Potential...

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Electric Potential Lecture 8.

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Electric Potential : Factor out the q! Analogy: F:E :: U:V V is the Electric Potential (V = Volt = J/C) U is the Electric Potential Energy (J) U Net , 0 = q 0 X i 6 =0 q i 4 ⇡✏ 0 r 0 ,i | {z } V = q 0 V F Net , 0 = q 0 X i 6 =0 q i ~ r i, 0 4 ⇡✏ 0 r 3 i, 0 | {z } ~ E = q 0 ~ E
What is electric potential (V) ? Common usage: What is the voltage (electric potential)? dU = V dQ Energy in batteries: Why is V so important? Voltage supplies Scalar

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Relation between E and V The E field is the negative gradient of the potential: Geometric meaning: Directional derivative Given a vector displacement, the Gradient tells you the derivative in that direction. Potential is the negative line integral of the E field: ~ E = - ~ r V = - ˆ i @ @ x + ˆ j @ @ y + ˆ k @ @ z V Δ V = - Z Γ d ~ ` · ~ E
Calculating V: Use superposition! V for a single point charge: … charge isn’t at origin: Multiple charges: Continuous distribution of charge: V ( ~ r ) = q 4 ⇡✏ 0 r V ( ~ r ) = q ~ r 0 4 ⇡✏ 0 | ~ r - ~ r 0 | V ( ~ r ) = Z dq ~ r 0 4 ⇡✏ 0 | ~ r - ~ r 0 | V ( ~ r ) = X i q i 4 ⇡✏ 0 | ~ r - ~ r i |

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Calculating V: V ( ~ r ) = X i q i 4 ⇡✏ 0 | ~ r - ~ r i |
Compute the potential from a ring of charge

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Compute the potential from a charged disk
Calculate V from E: Calculate the potential from a charged conducting sphere R Q

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