Question

3. A uniformly charged ring of radius, a, below. The net charge is positive. The location A is in The location B is a distance, a, directly above above the center of the ring. zed ring of radius, a, is situated horizontally, as shown Tge is positive. The location A is in the center of the ring. is a distance, a, directly above the center. Location C is very far a. Starting with the definition of the electric field, E = kaq, show that the electric field along the z axis of a charged ring is given by Ering 1 2Q "8 41€ (z? + R32 418, (2 b. At which location is the electric field the strongest? Explain. C. If the ring has a diameter of 10 cm and carries a charge of 18.0 nC. What is the electric field strength at a point B from the center of the ring? so

Answer 1

Cas k da dE 2 Sino comporents il concel dEsing alro da -Q 2TR 27Rr2 2 E 27R 27R 27R KOz ahere 4780 114 E = (4R NC

For moximum co x27 Z R fon point B E = = 9xlo2 (5x159)2 RO (RaR R 2 N/C 2.29 x10 E C

Answer 2

Solution 30 2dEcosa etende destino de sino as ата AS dE from all the components of the ring ie (du) suus upe Horizontal components gets cancelled out as they are equal & oppositely directed. vestical component sums up. Electric field can be written in either of the two ways ота I d E coso o 2dE so to ( k do caso , by geometery & I (224 22) ata Kdes 2 E² 42261942 प (kadez d (a²223/2 uña de En Kao 91% TO 279 or, E KZO (a²+ 22}}/2

(6) To find the place of the strongest electric field d E 2o have to be equated 2 dz de 20) = (OP7ZY 620 ()(642) 22 + Ke + 4 20 KO (827 22% 1-372 L (92479 - 32² = ofta2 92=222 10 jaar 5am a 5x10²m Q= 18x109 C 2200 5x15m E=kzo (92722/2 ke 5 x 9 E= 9x108x5x10²x 18 8109 al (5+1 634 (5x 1022 27 32 E= 22910 2597 N