Question

A straight, non-conducting plastic wire 8.50 cm long carries a charge density of 175 nC/m distributed uniformly along its length. It is lying on a horizontal tabletop. a) Find the magnitude and direction of

Answer 1

Answer:

$\mathbf{E = 3.04 \times 10^4 \ N/C}$ and the direction is vertically upward

Explanation:

To find the magnitude & direction which was being produced at a given point of 6.00 cm which is directly above the midpoint.

Given that:

the wire length = 8.50 cm = 8.5 × 10⁻² m

the charge density λ = 175 n C/m = 175 ×10⁻⁹ C/m

distance x = 6.00 cm = 0.006 m

Assume that  N be the point at distance x situated directly above the midpoint

Then, the linear expression for the linear charge density is:

$\lambda = \dfrac{Q}{L}$

the charge $Q = \lambda L$

$Q = 175 \times 10^{-9} \times 8. 5 \times 10^{-2}$

$Q = 1.49 \times 10^{-8} \ C$

For the electric field at point N;

$E = \dfrac {kQ}{x\sqrt{x^2 + r^2}}$

where;

$r = \dfrac{L} {2}$

$E = \dfrac {9\times 10^9 \times 1.49 \time 10^{-8} }{0.06 \times \sqrt{0.06^2 + (\dfrac{8.50 \times 10^{-2}}{2})^2}}$

$\mathbf{E = 3.04 \times 10^4 \ N/C}$