Q. 70 A thin cylindrical shell of radi... [FREE SOLUTION]

Chapter 23: Q. 70 (page 657)

A thin cylindrical shell of radius $R$ and length $L$ , like a soda straw, is uniformly charged with surface charge density $畏$ . What is the electric field strength at the center of one end of the cylinder?

Short Answer

Expert verified

The electric field strength at the center of one end of the cylinder is $\frac{畏}{2 蔚_{0}} [1 - \frac{R}{\sqrt{L^{2} + R^{2}}}]$

Step by step solution

Given information and formula used

Given :

Cylindrical shell has radius and length : $R and L$ respectively.

It is uniformly charged with surface charge density : $畏$

Theory used :

Charge on the cylinder is by:

$畏 = \frac{Q}{A} = \frac{Q}{2 蟺 R L} 鈬� Q = 2 蟺 R L 畏 (W h e r e i s A = 2 蟺 R L .)$
For all rings, use this formula:

$E_{r} = d E = \frac{1}{4 蟺蔚_{0}} \frac{3 d q}{{(z^{2} + R)}^{3 / 2}}$

Finding the electric field strength at the center of one end of the cylinder.

Now we integrate $E_{r} = d E$ :

role="math" localid="1649488487347" $E_{c} = 鈭� d E = \frac{1}{4 蟺蔚_{0}} {鈭�}_{0}^{L} \frac{z d q}{{(z^{2} + R)}^{3 / 2}} = \frac{1}{4 蟺蔚_{0}} {鈭�}_{0}^{L} 2 蟺 R 畏 \frac{z d z}{{(z^{2} + R)}^{3 / 2}} = \frac{R 畏}{2 蔚_{0}} {\frac{- 1}{\sqrt{z^{2} + R^{2}}}}_{0}^{L} = \frac{R 畏}{2 蔚_{0}} [\frac{- 1}{\sqrt{L^{2} + R^{2}}} - \frac{- 1}{R}] = \frac{畏}{2 蔚_{0}} [1 - \frac{R}{\sqrt{L^{2} + R^{2}}}]$

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91影视

A thin cylindrical shell of radius $R$ and length $L$ , like a soda straw, is uniformly charged with surface charge density $畏$ . What is the electric field strength at the center of one end of the cylinder?

Short Answer

Step by step solution

Given information and formula used

Finding the electric field strength at the center of one end of the cylinder.

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91影视

A thin cylindrical shell of radius Rand length L, like a soda straw, is uniformly charged with surface charge density 畏. What is the electric field strength at the center of one end of the cylinder?

Short Answer

Step by step solution

Given information and formula used

Finding the electric field strength at the center of one end of the cylinder.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Classical Mechanics

Physics of Motion

Translational Dynamics

Force

Medical Physics

Fundamentals of Physics

Study anywhere. Anytime. Across all devices.

A thin cylindrical shell of radius $R$ and length $L$ , like a soda straw, is uniformly charged with surface charge density $畏$ . What is the electric field strength at the center of one end of the cylinder?