Physics 16/21 Electromagnetism Equipotential Surface & Potential Gradient MARLON FLORES SACEDON Reminder: 4th Long exam: April 2, 2017 Sunday (2:00-4:00 PM)

Equipotential surface In electrostatics, the work done to move a charge from any point on the equipotential surface to any other point on the equipotential surface is zero since they are at the same potential. Furthermore, equipotential surfaces are always perpendicular to the net electric field lines passing through it.

Equipotential Topographic map

Equipotential In electrostatics, the work done to move a charge from any point on the equipotential surface to any other point on the equipotential surface is zero since they are at the same potential. Furthermore, equipotential surfaces are always perpendicular to the net electric field lines passing through it.

Potential gradient Definition of potential gradient. : the vector that represents the rate at which a potential changes with position in a specified direction; specifically : the rate of change with height of the atmospheric electric potential. then 𝑉 𝑎 − 𝑉 𝑏 = 𝑎 𝑏 𝐸 ∙𝑑 𝑙 −𝑑𝑉= 𝐸 𝑥 𝑑𝑥 𝐸 𝑥 =− 𝑑𝑉 𝑑𝑥 𝑦,𝑧 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 𝑉 𝑎 − 𝑉 𝑏 = 𝑏 𝑎 𝑑𝑉 =− 𝑎 𝑏 𝑑𝑉 then − 𝑎 𝑏 𝑑𝑉 = 𝑎 𝑏 𝐸 ∙𝑑 𝑙 −𝑑𝑉= 𝐸 ∙𝑑 𝑙 𝐸 = 𝐸 𝑥 𝑖 + 𝐸 𝑦 𝑗 + 𝐸 𝑧 𝑘 𝑑 𝑙 = 𝑖 𝑑𝑥+ 𝑗 𝑑𝑦+ 𝑘 𝑑𝑧 −𝑑𝑉= 𝐸 𝑥 𝑑𝑥+ 𝐸 𝑦 𝑑𝑦+ 𝐸 𝑧 𝑑𝑧 Suppose the displacement is parallel to x-axis 𝑑 𝑦 = 𝑑 𝑧 =0

Potential gradient Definition of potential gradient. : the vector that represents the rate at which a potential changes with position in a specified direction; specifically : the rate of change with height of the atmospheric electric potential.

Alternative solution 𝑟= 𝑥 2 + 𝑦 2 + 𝑧 2

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Answers to odd numbers

eNd