Question

A long straight metal rod has a radius of 5.00 cm anda charge per unit length of 30.0 nC/m. Find the electric field (a)3.00 cm, (b) 10.0 cm, (c) 100cm from the axis of the rod, wheredistances are measured perpendicular to the rod.

Answer 1

Answer:

given,

radius of rod = 5 cm

charge per unit length (λ) = 30.0 n C/m = 30 × 10⁻⁹ C/m

electric field duel to long straight wire =$E =\dfrac{\lambda}{2\pi \varepsilon\ r}$

a) distance = 3 + 5 = 8 cm

$E =\dfrac{30\times 10^{-9}}{2\pi \varepsilon\ 0.08}$

$\dfrac{1}{2\pi \varepsilon}$ = 18 × 10⁹

$E =\dfrac{30\times 10^{-9}\times 18 \times 10^{9}}{ 0.08}$

E = 6750 N/C

b) distance = 10 + 5 = 15 cm

$E =\dfrac{30\times 10^{-9}}{2\pi \varepsilon\ 0.15}$

$\dfrac{1}{2\pi \varepsilon}$= 18 × 10⁹

$E =\dfrac{30\times 10^{-9}\times 18 \times 10^{9}}{ 0.15}$

E = 3600 N/C

c) distance = 100 + 5 = 105 cm

$E =\dfrac{30\times 10^{-9}}{2\pi \varepsilon\ 1.05}$

$\dfrac{1}{2\pi \varepsilon}$ = 18 × 10⁹

$E =\dfrac{30\times 10^{-9}\times 18 \times 10^{9}}{ 1.05}$

E =514.28 N/C