How can we find the surface density on the surface of the conducting plate nearest to a point charge without using image method?
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we can find it by weighing its markful density on circuit apmphere of voltmere
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Hello mate here is your answer.
It's not zero.
Your textbook probably covers this, but the E⃗ E→ field is the gradient of a voltage field and a good conductor maintains a constant voltage; this constancy of voltage will "leak" somewhat to the space outside causing the voltage near the surface to be constant, too. This means that the E⃗ E→ field in the space around the conductor must point normal to it, near its surface.
There is an elegant way to solve this problem by simply trying to invent an imaginary charge distribution (the "method of image charges") inside of the conductor which, if the conductor were not there, would also guarantee that plane-of-constant-voltage and therefore E⃗ E→-normal-to-the-surface boundary condition. You may not 100% believe me on this, but if you do the math then the force on the one charge distribution due to the conductor must be exactly the force due to this "image charge distribution." This is a deep consequence of the principle of superposition and a statement of the uniqueness of the voltage field given its boundary conditions etc.
In this elegant way, one sees that for an infinite conductor spread out on the xyxy-plane, one can immediately cancel out the transverse components Ex,yEx,y of the electric field of a point charge QQ at (0,0,+z)(0,0,+z) by inventing an imaginary point charge −Q−Q at (0,0,−z)(0,0,−z), which would have the same EzEz component but negative Ex,yEx,y components on that plane. Therefore the force on the charge QQ due to the conductor is going to be just E⃗ =−z^ ke Q2/z2E→=−z^ ke Q2/z2 due to the Coulomb's law force between it and the imaginary charge.
Hope it helps you.
It's not zero.
Your textbook probably covers this, but the E⃗ E→ field is the gradient of a voltage field and a good conductor maintains a constant voltage; this constancy of voltage will "leak" somewhat to the space outside causing the voltage near the surface to be constant, too. This means that the E⃗ E→ field in the space around the conductor must point normal to it, near its surface.
There is an elegant way to solve this problem by simply trying to invent an imaginary charge distribution (the "method of image charges") inside of the conductor which, if the conductor were not there, would also guarantee that plane-of-constant-voltage and therefore E⃗ E→-normal-to-the-surface boundary condition. You may not 100% believe me on this, but if you do the math then the force on the one charge distribution due to the conductor must be exactly the force due to this "image charge distribution." This is a deep consequence of the principle of superposition and a statement of the uniqueness of the voltage field given its boundary conditions etc.
In this elegant way, one sees that for an infinite conductor spread out on the xyxy-plane, one can immediately cancel out the transverse components Ex,yEx,y of the electric field of a point charge QQ at (0,0,+z)(0,0,+z) by inventing an imaginary point charge −Q−Q at (0,0,−z)(0,0,−z), which would have the same EzEz component but negative Ex,yEx,y components on that plane. Therefore the force on the charge QQ due to the conductor is going to be just E⃗ =−z^ ke Q2/z2E→=−z^ ke Q2/z2 due to the Coulomb's law force between it and the imaginary charge.
Hope it helps you.
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