A uniform line charge extends from x = - 2.6 cm to x = + 2.6 cm and has a linear

Question

A uniform line charge extends from x = - 2.6 cm to x = + 2.6 cm and has a linear charge density of lambda = 63 nC/m. (a) Find the total charge. nC 0 attempt(s) made (maximum allowed for credit = 5) Find the electric field on the y axis at the following distances. (b) y = 4 cm N/C 0 attempt(s) made (maximum allowed for credit = 5) (c) y = 12 cm N/C 0 attempt(s) made (maximum allowed for credit = 5) (d) y =4.5m N/C 0 attempt(s) made (maximum allowed for credit = 5) (e) Find the field at y = 4.5 m, assuming the charge to be a point charge. N/C 0 attempt(s) made (maximum allowed for credit = 5)

Explanation / Answer

a)

= 6.3 x 10^-9 C/m
|x| = 2.6 cm (0.026m)

Q =  *x = 6.3 nC/m x 0.026 = 0.1638 nC

b)

= 6.3 x10^-9 C/m
y = 4 cm
|x| = 2.6 cm (0.026m)

E(p)= ((2k )/y) (|x|/y)

E(p) = ((2k )/y^2) |x|

E(p) = ((2 x 9 x 10^9 x 6.3 x 10^-9) / 0.04^2)*0.026

E(p) = 1843.75 N/C

c)

= 6.3 x10^-9 C/m
y = 12 cm
|x| = 2.6 cm (0.026m)

E(p)= ((2k )/y) (|x|/y)

E(p) = ((2k )/y^2) |x|

E(p) = ((2 x 9 x 10^9 x 6.3 x 10^-9) / 0.12^2)*0.026

E(p) = 204.75 N/C

d)

= 6.3 x10^-9 C/m
y = 4.5 m
|x| = 2.6 cm (0.026m)

E(p)= ((2k )/y) (|x|/y)

E(p) = ((2k )/y^2) |x|

E(p) = ((2 x 9 x 10^9 x 6.3 x 10^-9) / 4.5^2)*0.026

E(p) = 0.1456 N/C

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