Question

The charge per unit length on a long, straight line is -90 μC/m. The electric field at 10 cm from the line, where the distance is measured perpendicular to the length of the line (in N/C):

a) -900 N/C
b) 900 N/C
c) -9 N/C
d) 9 N/C

Answer 1

The electric field due to a charged line where the charge per unit length is -90 µC/m and at a distance of 10 cm from it is 900 N/C, directed towards the line.

Step-by-step explanation:

The question involves calculating the electric field due to a uniformly charged long, straight line. As the charge is negative (-90 µC/m), the electric field lines will be directed towards the line. The formula for the electric field (E) due to a linear charge distribution is E = λ/(2πε0r), where λ is the charge per unit length, ε0 is the permittivity of free space, and r is the radial distance from the line. Plugging in λ = -90 µC/m = -90×10-6 C/m and r = 10 cm = 0.1 m, we find the electric field as a negative value, showing that it is directed radially towards the line.

Therefore, the correct answer from the provided options is (b) 900 N/C, with the understanding that the negative sign indicates the direction of the electric field towards the line of charge.