A uniform line charge of linear charge density ? = 4.7 nC/m extends from x = 0 t

Question

A uniform line charge of linear charge density  ? = 4.7 nC/m extends from x = 0 to x = 5 m.

(a) What is the total charge?

nC

(b) Find the electric field on the x axis at x = 6 m.

N/C

(c) Find the electric field on the x axis at x = 8 m.

N/C

(d) Find the electric field on the x axis at x = 260 m.

N/C

(e) Find the field at x = 260 m, using the approximation that the charge is a point charge at the origin.

N/C

Compare your result with that for the exact calculation in part (d).

(field for the point charge divided by the field for the line charge)

GIVE EXACT ANSWERS FOR ALL PARTS PLZ

Explanation / Answer

lets take a small length element dx, q is the total charge, l is total length, a is distance from nearer end.
dq=(q/l)dx

dE=dq/{4pie0(a+x)^2 }
substitute for dq:

dE = qdx / {4pi e0 l(a+x)^2}

E = q / 4pi e0 (a+x) ^(-2)dx (integrating giving proper limits upper limit=l, lower limit= 0)

E=q / {4pi e0(a+l)}

solve for total charge q= 4.7 nC/m*5m= 23.5nC,

E at 6m is l = 5m, a = 6 - 5 = 1m

E == 23.5 *10^-9./ 4*3.14* 8.85*10^-12 * 6 = 35.2 N/C

E at 10m is l=5, a= 5 m

E = 23.5*10^13/4pi 8.85*10^-12*10 = 21.1 N/C

E at 260 m = 13nC/4pi 8.85*10^-12 *290 = 0.729 N/C

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