204B (FALL 2018) hussain Problem Set 01 Problem 5 K55 A total charge is uniforml

Question

204B (FALL 2018) hussain Problem Set 01 Problem 5 K55 A total charge is uniformly distributed along a thin, flexible insulating strip of length L. The strip is then bent into the semicircle shown in the figure (Figure 1) Part A Find a symbolic expression for the electric field E at the oenter of the semicircle Hint: A small piece care length s spans a small angle s /R, where R is the radius. Express your answer in terms of the varlables Q, L, unit vectors i, 3, and appropriate constants. Submit Part B Figure 1 of Compute the strength of this field if L = 19 cm and Q-25 nC Express your answer with the appropriate units. ? Center Value Units Submit Request Answer

Explanation / Answer

Given

the semicircle with charge Q which is uniformly distributed

and of length L = pi*r ==> r = L/pi

where r is the radius of the circle

here by symmetry the x component of the electric field will cancel from the different portions of the small strips along the circumferance  

only y component will exist

we know that the electric field at the center of the semi circle is  

Ey = 2*k*Q/(pi*r^2)

Ey = 2*k*Q/(pi*(L/pi)^2)

Ey = 2*k*Q*pi/L^2

E = Ex i + Ey j

E =0 i + (2*k*Q*pi/L^2)j

Part B

L = 19 cm = 0.19m

Q = 25 nC

substituting the values

E y = 2*9*10^9*25*10^-9*pi/(0.19^2) N/C

Ey = 39161.127 N/C

E = Ex i + Ey j

E = 0 N/C i + 39161.127 N/C j

the magnitude is E = sqrt(Ex^2+Ey^2)

E = sqrt(0^2+39161.127^2) N/C

E = 39161.127 N/C

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