Chapter 15: Q15CP (page 594)

If the total charge on a thin rod of length $0.4$ is $2.5 nC$ , what is the magnitude of the electric field at a location $1 Cm$ from the midpoint of the rod, perpendicular to the rod?

Short Answer

Expert verified

$1.12 \times 10^{4} N / C$

Step by step solution

Identification of the given data

The given data is listed below as-

The length of the thin rod is, $L = 0.4 m$
The charge of the thin rod is,
The location of the electric field is,

Significance of the electric field

The electric field is a region in which a charged particle is able to exert force on another charged particle.

The concept of the electric field gives the magnitude of the electric field.

Determination of the magnitude of the electric field

The equation of the magnitude of the electric field is expressed as,

$E = \frac{1}{4 {πε}_{0}} (\frac{Q}{\sqrt[X]{X^{2} + {(\frac{L}{2})}^{2}}})$

Here, $\frac{1}{4 {πε}_{0}}$ is the constant of electric field, $Q$ is the charge of the thin rod, $X$ is the location of the electric field and $L$ is the length of the thin rod.

For $\frac{1}{4 {πε}_{0}} = 8.99 \times 10^{9} N . M / C^{2}$ , $Q = 2.5 nC$ , $X = 1 cm$ and $L = 0.4 m$ .

$E = 8.99 \times 10^{9} N . m^{2} / c^{2} \times (\frac{25 nC}{\sqrt[1 cm]{{(1 cm)}^{2} + {(\frac{0.4 m}{2})}^{2}}})$

$= 8.99 \times 10^{9} N . m^{2} / C^{2} \times (\frac{2.5 nC \times \frac{1 \times 10^{- 9} C}{1 nC}}{1 cm \times \frac{1 m}{100 cm} \sqrt{{(1 cm \times \frac{1 m}{100 cm})}^{2} + {(\frac{0.4 m}{2})}^{2}}})$

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If the total charge on a thin rod of length $0.4$ is $2.5 nC$ , what is the magnitude of the electric field at a location $1 Cm$ from the midpoint of the rod, perpendicular to the rod?

Short Answer

Step by step solution

Identification of the given data

Significance of the electric field

Determination of the magnitude of the electric field

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Most popular questions from this chapter

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If the total charge on a thin rod of length 0.4is2.5nC, what is the magnitude of the electric field at a location1Cmfrom the midpoint of the rod, perpendicular to the rod?

Short Answer

Step by step solution

Identification of the given data

Significance of the electric field

Determination of the magnitude of the electric field

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Thermodynamics

Physical Quantities And Units

Electromagnetism

Work Energy and Power

Rotational Dynamics

Physics of Motion

Study anywhere. Anytime. Across all devices.

If the total charge on a thin rod of length $0.4$ is $2.5 nC$ , what is the magnitude of the electric field at a location $1 Cm$ from the midpoint of the rod, perpendicular to the rod?