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85. Electric Field and Electric Potential

85. Electric Field and Electric Potential - ⇔ V x =-Z x x...

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Electric Field and Electric Potential Determine the field or the potential from the source (charge distribution): ~ E = 1 4 π 0 Z dq r 2 ˆ r r dE dV r dq V = 1 4 π 0 Z dq r Determine the field from the potential: ~ E = - ∂V ∂x ˆ i - ∂V ∂y ˆ j - ∂V ∂z ˆ k Determine the potential from the field: V = - Z ~ r ~ r 0 ~ E · d~ s Systems with uniaxial symmetry: E x ( x ) = - dV
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Unformatted text preview: ⇔ V ( x ) =-Z x x E x dx • Application to charged ring: E x = kQx ( x 2 + a 2 ) 3 / 2 ⇔ V = kQ √ x 2 + a 2 • Application to charged disk (at x > ): E x = 2 πσk » 1-x √ x 2 + R 2 – ⇔ V = 2 πσk h p x 2 + R 2-x i tsl85 – p.1/1...
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