A long thin wire, hundreds of meters long, carries a uniformly distributed charg

Question

A long thin wire, hundreds of meters long, carries a uniformly distributed charge of -4.5 mu C per meter of length. Estimate the magnitude of the electric field at point 5.5 m perpendicular from the center of the wire. Express your answer using two significant figures. Estimate the direction of the electric field at point 5.5 m perpendicular from the center of the wire. towards the wire outwards the wire Estimate the magnitude of the electric field at point 1.0 m perpendicular from the center of the wire. Express your answer using two significant figures. Estimate the direction of the electric field at point 1.0 m perpendicular from the center of the wire. outwards the wire towards the wire

Explanation / Answer

here,
charge density of wire, Lamda = -4.5 uC/m = -4.5*10^-6 C/m

From gauss law , Electric Field on wire from a point is given as :

E = lamda/(2*pi*eo*r)
where
lambda is linear charge density,
eo is electric permittivity
r is the perpendicular distance

Part A:
at r = 5.5 m

E = lamda/(2*pi*eo*r)
E = (-4.5*10^-6)/(2*3.14*8.85*10^-12*5.5)
E = -1.47*10^4 N/C

Part B:
Towards wire as charge density is negative

Part C:
at r = 1 m

E = lamda/(2*pi*eo*r)
E = (-4.5*10^-6)/(2*3.14*8.85*10^-12*1)
E = -8.1*10^4 N/C

Part D:
Towards Wire as charge density is negative

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