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

2. E-field of a thin disk Available :
A thin circular disk with radius R and charge density s [C/m2]
Question :
Calculate E-field in arbitrary points a both sides of the disk
E-field of a thin disk

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

4. Analysis and Symmetry 1. Charge distribution: s [C/m2]
2. Coordinate axes:
Z-axis = symm. axis,
perpend. to disk Z X Y ej j er r ez z
3. Symmetry: cylinder
4. Cylinder coordinates:
r, z, j
E-field of a thin disk

5. Analysis, field build-upR Ei Qi ri
3. all Qi’s at ri and ji contribute Ei to E in P
1. XYZ-axes Z Y X
2. Point P on Y-axis P
4. Ei,xy , Ei,z
Ei,z
Ei,xy
5. expect: S Ei,xy = 0,
to be checked !!
6. E = Ez ez only !
E-field of a thin disk

6. Approach to solution R Z 1. Rings and segments 2. Distributed chargesdQ 3. dE er r P
4. dQ = s.dA= s (da.)(a dj) a dj j da
5. z- component only !
dExy
dEz 6.
E-field of a thin disk

7. Calculations (1) R Z dQ dE er r P a dj j da dEz zP 1.
2. dQ = s.dA= s (da.)(a dj) 3. 4.
E-field of a thin disk

8. Calculations (2) R Z dQ dE er r P a dj j da dEz zP 4.
6. If R -> infinity :
E-field of a thin disk

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

10. Appendix: angular integration (1)Z dQ dE er r P a dj j da
dEz zP 1.
2. dQ = s.dA= s (da.)(a dj) 3.
E-field of a thin disk

11. Appendix: angular integration (2)Z dQ dE er r P a dj j da
dEz zP 3.
the end
E-field of a thin disk