- #1
Redoctober
- 48
- 1
So here is the scenario (see attachment) - I have a semicircle wire (radius R=15.9cm) which is made of insulator material , the semicircle consist of two combined quartercircle wires parts where one has equally distributed charge +Q and the other has -Q . Required is find the Electric field in direction of x at the origin . Q=5.33nC
My approach was as follows
Let E = 1/(4*pi*e)∫1/(R^2).dQ r
dQ=λ*ds and ds=R*dθ and i also know that unit vector r = cosθ*i+sinθ*j
therefore for the E in x direction i get this expression
E = 1/(4*pi*e)*1/(R^2)*λ*R∫cosθ.dθ
Integrating from 0 to pi ( thus taking only half of the semicircle ) and using λ as 2/(pi*r)
I get Q/(2*pi^2*e*R^2) .
Because the other half has opposite charge i can say that the Etot = Eneg +Epos
Therefore i multiply the equation by two to finaly get
Q/(pi^2*e*R^2)
If i put the values given i get as absolute value 2413 N/C for Electric field at origin of circel in the direction of x
Unfortunately it is a wrong solution :( ! What is the mistake i hv done ?? Can anyone spot it ? Thanks in advance
My approach was as follows
Let E = 1/(4*pi*e)∫1/(R^2).dQ r
dQ=λ*ds and ds=R*dθ and i also know that unit vector r = cosθ*i+sinθ*j
therefore for the E in x direction i get this expression
E = 1/(4*pi*e)*1/(R^2)*λ*R∫cosθ.dθ
Integrating from 0 to pi ( thus taking only half of the semicircle ) and using λ as 2/(pi*r)
I get Q/(2*pi^2*e*R^2) .
Because the other half has opposite charge i can say that the Etot = Eneg +Epos
Therefore i multiply the equation by two to finaly get
Q/(pi^2*e*R^2)
If i put the values given i get as absolute value 2413 N/C for Electric field at origin of circel in the direction of x
Unfortunately it is a wrong solution :( ! What is the mistake i hv done ?? Can anyone spot it ? Thanks in advance