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By symmetry, the components of (Er) in the direction of (ăr ) will add up to zero, because for every element of (dl) in one half of the circle there is a corresponding component of (dEr)and in the other half there is a symmetric component of (Er) but with opposite direction, so they cancel each other. Therefore (Er) component is (zero) and only (Ez) is exist. That is: Pi ah 4neo[h² + a²j°/2 Jo 2n E = dø ăz Then Pi ah ăz 2€0[h²+a²j®/½ E = H.W.1: A circular ring has ( pl =4 uC/m) of radius (3m) ,its center at origin on (xy-plane). Find (E ) at:a) (0,0,6), b) at (0,0, -6), c) at origin.

By symmetry, the components of (Er) in the direction of (ăr ) will add up to zero, because for every element of (dl) in one half of the circle there is a corresponding component of (dEr)and in the other half there is a symmetric component of (Er) but with opposite direction, so they cancel each other. Therefore (Er) component is (zero) and only (Ez) is exist. That is: Pi ah 4neo[h² + a²j°/2 Jo 2n E = dø ăz Then Pi ah ăz 2€0[h²+a²j®/½ E = H.W.1: A circular ring has ( pl =4 uC/m) of radius (3m) ,its center at origin on (xy-plane). Find (E ) at:a) (0,0,6), b) at (0,0, -6), c) at origin.

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By symmetry, the components of (Er) in the direction of (år ) will add up to zero, because for every element of (dl) in one half of the circle there is a corresponding component of (dEr)and in the other half there is a symmetric component of (Er) but with opposite direction, so they cancel each other. Therefore (Er) component is (zero) and only (Ez) is exist. That is: Pi ah E = 4nEo[h? + a?1%% J, dø ă, Then E = PL ah ăz 2€0[h²+a²j®/½ H.W.1: A circular ring has ( pl 4 µC/m) of radius (3m) ,its center at origin on (xy-plane). Find (E) at:a) (0,0,6), b) at (0,0, -6), c) at origin.
Transcribed Image Text:By symmetry, the components of (Er) in the direction of (år ) will add up to zero, because for every element of (dl) in one half of the circle there is a corresponding component of (dEr)and in the other half there is a symmetric component of (Er) but with opposite direction, so they cancel each other. Therefore (Er) component is (zero) and only (Ez) is exist. That is: Pi ah E = 4nEo[h? + a?1%% J, dø ă, Then E = PL ah ăz 2€0[h²+a²j®/½ H.W.1: A circular ring has ( pl 4 µC/m) of radius (3m) ,its center at origin on (xy-plane). Find (E) at:a) (0,0,6), b) at (0,0, -6), c) at origin.
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