Chapter 10: Q75E (page 473)

Question: The magnetic field at the surface of a long wire radius R and carrying a current I is $\frac{μ_{0} I}{2 π R}$ . How large acurrent could a 0.1 mm diameter niobium wire carry without exceeding its 0.2 T critical field?

Short Answer

Expert verified

Answer

Current in the wire is 50A.

Step by step solution

Given data

Diameter of niobium wire is, 0.1mm .

Maximum magnetic field is,0.2T .

Step 2: Formula of Magnetic Field produced by a Wire

given by, $B = \frac{μ_{0} I}{2 π R}$ .

Here I represents current, R represents radius of wire and $μ_{0}$ represents permeability of free space.

Calculate the Current from the Expression of Magnetic Field produced by a Wire

The radius of the wire is, $R = \frac{D}{2}$ .

Substitute $0.1 mm \to D$ and convert it into m .

$R = \frac{D}{2} = \frac{0.1 mm}{2} = 0.05 mm (\frac{10^{- 3} m}{1 mm}) = 0.05 \times 10^{- 3} m$

The magnetic field produced by the current is given by, $B = \frac{μ_{0} I}{2 π R}$ .

Rearrange the above equation for l .

$B = \frac{μ_{0} I}{2 π R}$

Substitute $4 π \times 10^{- 7} T \cdot m / A \to μ_{0}, 0.2 T \to B$ , and $0.05 \times 10^{- 3} m \to R$ in the above equation.

$B = \frac{μ_{0} I}{2 π R} I = \frac{2 π R B}{μ_{0}} = \frac{2 π (0.05 \times 10^{- 3} m) (0.2 T)}{4 π \times 10^{- 7} Tm/A} = 50 A$

Current in the wire is 50 A .

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Question: The magnetic field at the surface of a long wire radius R and carrying a current I is $\frac{μ_{0} I}{2 π R}$ . How large acurrent could a 0.1 mm diameter niobium wire carry without exceeding its 0.2 T critical field?

Short Answer

Step by step solution

Given data

Step 2: Formula of Magnetic Field produced by a Wire

Calculate the Current from the Expression of Magnetic Field produced by a Wire

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Question: The magnetic field at the surface of a long wire radius R and carrying a current I is μ0I2πR . How large acurrent could a 0.1 mm diameter niobium wire carry without exceeding its 0.2 T critical field?

Short Answer

Step by step solution

Given data

Step 2: Formula of Magnetic Field produced by a Wire

Calculate the Current from the Expression of Magnetic Field produced by a Wire

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Thermodynamics

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Study anywhere. Anytime. Across all devices.

Question: The magnetic field at the surface of a long wire radius R and carrying a current I is $\frac{μ_{0} I}{2 π R}$ . How large acurrent could a 0.1 mm diameter niobium wire carry without exceeding its 0.2 T critical field?