Chapter 23: Q. 42 (page 655)

FIGURE is a cross section of two infinite lines of charge that extend out of the page. The linear charge densities are $\pm λ$ . Find an expression for the electric field strength $E$ at height $y$ above the midpoint between the lines.

Short Answer

Expert verified

The expression for electrical field strength, $E = \frac{2 λ d}{π ϵ_{o} (d^{2} + 4 y^{2})} .$

Step by step solution

Step1: Definition of Electrical charge:

Charges that are similar repel one other, while charges that are dissimilar attract one other. when matter is placed in an electromagnetic field, an electric charge, which causes it to experience a force. A positive or negative charge can exist (commonly carried by protons and electrons respectively).

Find the Electrical charge

Electrical field make to horizontal component by infinite lines of charge density $λ$

$E_{x} = 2 E_{x} \sin θ$

$(\sin θ = \frac{d}{2 \sqrt{\frac{d^{2}}{4} + y^{2}}})$

$E = \frac{λ}{2 π ϵ_{o} l}$

$(l = \sqrt{\frac{d^{2}}{4} + y^{2}})$

$E_{x} = 2 \times \frac{λ}{2 π ϵ_{o} l} \times \frac{d}{2 l}$

$E = \frac{λ d}{π ϵ_{o} 2 \times \frac{1}{4} (d^{2} + y^{2} 4)}$

$E = \frac{2 λ d}{π ϵ_{o} (d^{2} + 4 y^{2})}$

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FIGURE is a cross section of two infinite lines of charge that extend out of the page. The linear charge densities are $\pm λ$ . Find an expression for the electric field strength $E$ at height $y$ above the midpoint between the lines.

Short Answer

Step by step solution

Step1: Definition of Electrical charge:

Find the Electrical charge

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FIGURE is a cross section of two infinite lines of charge that extend out of the page. The linear charge densities are ±λ. Find an expression for the electric field strength Eat height yabove the midpoint between the lines.

Short Answer

Step by step solution

Step1: Definition of Electrical charge:

Find the Electrical charge

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Electric Charge Field and Potential

Thermodynamics

Space Physics

Medical Physics

Quantum Physics

Magnetism

Study anywhere. Anytime. Across all devices.

FIGURE is a cross section of two infinite lines of charge that extend out of the page. The linear charge densities are $\pm λ$ . Find an expression for the electric field strength $E$ at height $y$ above the midpoint between the lines.