Define electric potential at a point using a test charge and an infinity reference. An external agent does −4.0 μJ while bringing +2.0 nC slowly from infinity to P. Find the potential and explain the negative sign.

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External work per unit small positive test charge brought from infinity with no kinetic-energy change; V = −2.0 kV; the field assists the transfer. State external work per unit positive test charge, from infinity to the point. Include the small-test-charge assumption and slow motion/no kinetic-energy change. V = −4.0 × 10⁻⁶/(2.0 × 10⁻⁹) = −2.0 × 10³ V. The electric field does positive work on the positive charge; the external agent removes energy to prevent acceleration.

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Define electric potential at a point using a test charge and an infinity reference. An external agent does −4.0 μJ while bringing +2.0 nC slowly from infinity to P. Find the potential and explain the negative sign.

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