A straight, nonconducting plastic wire 9.00 cm long carries a charge density of

Question

A straight, nonconducting plastic wire 9.00 cm long carries a charge density of 100 nC/m distributed uniformly along its length. It is lying on a horizontal tabletop

Part A

Find the magnitude and direction of the electric field this wire produces at a point 4.00 cm directly above its midpoint.

Part B

If the wire is now bent into a circle lying flat on the table, find the magnitude and direction of the electric field it produces at a point 4.00 cm directly above its center.

both answers should be in N/C

Explanation / Answer

Linear Charge Density

lambda = Q/L

Q = lambda * L = 100*10^(-9)*0.09 = 9*10^(-11) C

A)

electric field E = kQ/(x*sqrt(x^2 + a^2))

E = 9*10^9*9*10^(-11)/[0.04*sqrt(0.04^2 + (0.09/2)^2)] = 336.38 N/C

Electric field is Directed upwards since it has only component in x-direction

B)

electric field E = kQx/(x^2 + a^2)^(3/2)

E = 9*10^9*9*10^(-11)*0.04/[(0.04^2 + (0.09/(2*3.24))^2)] = 17.94 N/C

Electric field is Directed upwards since it has only component in x-direction

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