Question

An infinite line of charge with linear density λ1 = 6 μC/m is positioned along the axis of a thick insulating shell of inner radius a = 2.6 cm and outer radius b = 4.2 cm. The insulating shell is uniformly charged with a volume density of rho = -634 μC/m3. What is λ2, the linear charge density of the insulating shell?

Answer 1

Answer: λ2= 2.34 * 10^-6 C/m

Explanation: In order to calculate the value of the  linear charge density of the insulating shell we have to multiply ρ* Volume of the hollow cylinder, so

Volume of cylinder:2*π*b*L *(b-a)  where (b-a) is the thickness, then

λ2=Q/L = 634 *10^-6 C/m^3* 2*π*0.042 m*(0.042-0.26)== 2.34 μ C/m

Answer 2

The linear charge density of the insulating shell due to infinite line of charge is -2.3 μC/m.

What is linear charge density?

The linear charge density of a insulating shell, is the amount of charge present in the shell per unit length. The linear charge density, for the insulating shell, can be given as,

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

Here, (Q) is the charge and (L) is the length of hte shell.

If the volume density($\rho$) and the inner(a) and outer(b) radius of the cylindric shell is given, then the  linear charge density can be given as,

$\lambda=\rho\pi(b^2-a^2)$

It is given that the, for an infinite line of charge with linear density λ1 = 6 μC/m. The inner radius and the outer radius of the insulating shell is is 2.6 cm and 4.2 cm respectively. '

As, the insulating shell is uniformly charged with a volume density -634 μC/m3. Thus, the linear charge density of the insulating shell can be find out using the above formula as,

$\lambda_2=-653 \times\pi((0.042)^2-(0.026)^2)\\\lambda_2=-2.3\rm \mu C/m$

Thus the linear charge density of the insulating shell due to infinite line of charge is -2.3 μC/m.

Learn more about the linear charge density here;

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