Chapter 27: Q. 39 (page 763)

For what electric field strength would the current in a $2.0 m m$ diameter nichrome wire be the same as the current in a $1.0 m m$ diameter aluminum wire in which the electric field strength is $0.0080 V / m$ ?

Short Answer

Expert verified

The electric field strength is $0.104 V / m$ .

Step by step solution

Given Information

Nichrome wire diameter $= 2.0 m m$

Aluminum wire diameter $= 1.0 m m$

Electric field strength $= 0.0080 V / m$

Explanation

Express the electric field strength as,

$J = σ E \Rightarrow E = \frac{J}{σ}$

Electric current density is,

$J = \frac{I}{A}$

Here, the cross-sectional area is a circle,

$J = \frac{4 I}{π D^{2}} .$

Combining the expression,

$E = \frac{4 I}{π σ D^{2}},$

So, the product $E π σ D^{2}$ will be constant for both wires.

Simplify the $π,$

$E_{1} σ_{1} D_{1}^{2} = E_{2} σ_{2} D_{2}^{2}$

The aluminum is represented by $1$ and the nichrome is represented by $2$ .

In the case of the nichrome, the electric field is calculated as follows:

$E_{2} = \frac{σ_{1}}{σ_{2}} {(\frac{D_{1}}{D_{2}})}^{2} E_{1}$

Substitute the expression,

localid="1649072796279" $E_{2} = (\frac{350 s}{6.7 s} \times 0 . 5^{2} m m \times 0.008 V / m)$

localid="1649072915118" $= 0.104 V / m$

Final Answer

Hence, the electric field strength will be $104 m V / m .$

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For what electric field strength would the current in a $2.0 m m$ diameter nichrome wire be the same as the current in a $1.0 m m$ diameter aluminum wire in which the electric field strength is $0.0080 V / m$ ?

Short Answer

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Given Information

Explanation

Final Answer

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For what electric field strength would the current in a 2.0mmdiameter nichrome wire be the same as the current in a 1.0mmdiameter aluminum wire in which the electric field strength is0.0080V/m?

Short Answer

Step by step solution

Given Information

Explanation

Final Answer

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Astrophysics

Energy Physics

Dynamics

Modern Physics

Conservation of Energy and Momentum

Electromagnetism

Study anywhere. Anytime. Across all devices.

For what electric field strength would the current in a $2.0 m m$ diameter nichrome wire be the same as the current in a $1.0 m m$ diameter aluminum wire in which the electric field strength is $0.0080 V / m$ ?