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E-field of a thin disk1 Electrical Field of a thin Disk © Frits F.M. de Mul

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E-field of a thin disk2 Available : A thin circular disk with radius R and charge density [C/m 2 ] Available : A thin circular disk with radius R and charge density [C/m 2 ] Question : Calculate E-field in arbitrary points a both sides of the disk Question : Calculate E-field in arbitrary points a both sides of the disk

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E-field of a thin disk3 Analysis and symmetry Approach to solution Calculations Conclusions Appendix: angular integration

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E-field of a thin disk4 Analysis and Symmetry 1. Charge distribution: C/m 2 ] 2. Coordinate axes: Z-axis = symm. axis, perpend. to disk Z X Y 3. Symmetry: cylinder 4. Cylinder coordinates: r, z erer r ezez z e

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E-field of a thin disk5 Analysis, field build-up R 1. XYZ-axes Z Y X 2. Point P on Y-axis P EiEi QiQi riri 3. all Q is at r i and i contribute E i to E in P 4. E i,xy, E i,z E i,z E i,xy 5. expect: E i,xy = 0, to be checked !! 6. E = E z e z only !

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E-field of a thin disk6 Approach to solution R Z 2. Distributed charges dQ 3. dE erer r P 1. Rings and segments 4. dQ = dA= da.)(a d a d da 5. z- component only ! dE xy dE z 6.

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E-field of a thin disk7 Calculations (1) R Z dQ dE erer r P a d da dE z zPzP dQ = dA= da.)(a d 3. 4.

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E-field of a thin disk8 Calculations (2) R Z dQ dE erer r P a d da dE z zPzP If R infinity :

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E-field of a thin disk9 Conclusions Z P EPEP for infinite disk: field strength independent of distance to disk => homogeneous field

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E-field of a thin disk10 Appendix: angular integration (1) R Z dQ dE erer r P a d da dE z zPzP dQ = dA= da.)(a d

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E-field of a thin disk11 Appendix: angular integration (2) R Z dQ dE erer r P a d da dE z zPzP the end

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