Question

20. A cylinder is charged by 10 mC. Length of the cylinder is 1km and radius is 1mm . Surface density of charge of

cylinder is

a. 1.59 x 10 -4 C/m2

b. 1.59 x 10-2 C/m2

c. 1.59 x 10-3 C/m2

d. 1.59 x 10-5 C/m2​

Answer 1

Given :

• Charge on cylinder $q = 10 mC$
• Length of cylinder $L = 1 km = 1000 m$
• Radius of cylinder $r = 1 mm = 10^{-3} m$

To Find :

• Surface charge density $(\sigma)$

Solution :

We know that, surface charge density is given by the charge per unit surface area

   ∴                 $\sigma = \frac{q}{area}$

Surface Area of cylinder is given by ,

                       $A = \pi r^2 L$

                    $A = \pi \times ( 10^{-3} )^2 \times (10^3)$

                   $A = \pi \times 10^{-3} m^2$

Now,

                  $\sigma = \frac{10 \times 10^{-3}}{\pi \times 10^{-3}}$

                  $\sigma = \frac{10 \times 7 }{22}$

                  $\sigma = 3.18 C/m^2$

Thus,  Surface charge density $\sigma = 3.18 C/m^2$