Question

A 2-m long thin and straight metal wire carries a positive charge of 3 µ C. (a) What is the linear charge density on the wire? (b) Hence, find the electric intensity at a point 1.5 m away from the centre of the wire.

Answer 1

Data: q = 3 µC = 3 × 10⁻⁶ C, l = 2 m, r = 1.5 m, π = 3.142, and ε₀ = 8.85 × 10⁻¹² C²/N.m²

Charge density, λ = ${\displaystyle \frac{q}{l}}$

= ${\displaystyle \frac{3\times {10}^{-6}}{1.5}}$

= 2 × 10⁻⁶ C/m

Electric intensity, E = ${\displaystyle \frac{\lambda }{2\pi {\epsilon }_{0}r}}$

= ${\displaystyle \frac{2\times {10}^{-6}}{2\left(3.142\right)(8.85\times {10}^{-12})\left(1.5\right)}}$

= ${\displaystyle \frac{{10}^6}{3.142\times 8.85\times 1.5}}$

log 3.142     0.4972
log 8.85    + 0.9469
log 1.5      + 0.1761
                    1.6202
log 10⁶        6.0000
                 − 1.6202
                    4.3798

antilog 4.3798 = 2.397

= 2.397 × 10⁴ N/C