13. [lpt] A thin rod, 56.0 cm long, is charged uniformly with a positive charge

Question

13. [lpt] A thin rod, 56.0 cm long, is charged uniformly with a positive charge density of 77.7 C/m. The rod is placed along the y axis and is centered at the origin. A charge of +47.5 is placed 834 cm from the midpoint of the rod on the positive x axis. Calculate the electric field at the point on the x axis that is halfway between the point charge and the centre of the rod. (Note: the field is positive if it is in the direction of X.) Answer: Submit All Answers Last Answer: 9.63E-15 N/C Incorrect, tries 7/15

Explanation / Answer

given data

L = 56 cm = 0.56 m

lamda = 77.7 micro C/m

q = 47.5 micro C

distance from rod to the mid point, d = 83.4/2

= 41.7 cm

= 0.417 m

electric field due to rod at mid point,

E_rod = (k*lamda/d)*(L/sqrt(L^2/4 + d^2))

= (9*10^9*77.7*10^-6/0.417)*(0.56/sqrt(0.56^2/4 + 0.417^2) )

= 1.87*10^6 N/c (towards +x axis)

electric field due to point charge

Eq = k*q/d^2

= 9*10^9*47.5*10^-6/0.417^2

= 2.46*10^6 N/c (towards -x axis)

so, net electric field,

Enet = -(Eq - Erod)

= -(2.46*10^6 - 1.87*10^6)

= -5.9*10^5 N/c <<<<<<<---------------------Answer

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