A total charge Q = -1.3 mu C ts distributed uniformly over a quarter circle arc

Question

A total charge Q = -1.3 mu C ts distributed uniformly over a quarter circle arc of radius a = 6.1 cm as shown. What is lambda the linear charge density along the arc? ____________ C/m What is E_x, the value of the x-component of the electric field at the origin (x, y) = (0, 0)? ____________ N/C What is E_y, the value of the y-component of the electric field at the origin (x, y) = (0, 0) ? _________ N/C How does the magnitude of the electric field at the origin for the quarter-circle are you have just calculated compare to the electric field at the origin produced by a point charge Q = -1.3 mu C located a distance a = 6.1 cm from the origin along a 45degree line as shown in the figure? The magnitude of the field from the point charge is less than that from the quarter-arc of charge. The magnitude of the field from the point charge is equal to that from the quarter arc of charge. The magnitude of the field from the point charge H greater than that from the quarter-arc of charge What is the magnitude of the electric field at the origin produced by a semi-circular arc of charge = -2.6 mu C, twice the charge of the quarter-circle are? ___________ N/C

Explanation / Answer

1) lamda = Q/L

= Q/(pi*r/2)

= 2*Q/(pi*r)

= 2*-1.3*10^-6/(pi*0.061)

= -1.4*10^-5 C/m

2) Ex = k*lamda/R

= 9*10^9*1.4*10^-5/0.061

= 2.1*10^6 N/c

3)
Ey = k*lamda/R

= 9*10^9*1.4*10^-5/0.061

= 2.1*10^6 N/c

4) 3rd option is correct

5)

Ex = Ey = 2*2.1*10^6

= 4.2*10^6 N/c

Enet = sqrt(Ex^2 + Ey^2)

= sqrt(2)*4.2*10^6

= 5.9*10^6 N/c

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