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Chapter 26: Problem 27

You're on a team performing a high-magnetic-field experiment. A conducting bar carrying 4.1 kA will pass through a 1.3-m-long region containing a 12 -T magnetic field, making a \(60^{\circ}\) angle with the field. A colleague proposes resting the bar on wooden blocks. You argue that it will have to be clamped in place, and to back up your argument you claim that the magnetic force will exceed 10,000 pounds. Are you right?

Short Answer

Expert verified
No, the claim is incorrect. The calculated magnetic force on the bar is 7687.546 lb, which is less than 10000 pounds.

Step by step solution

01

Identify the values

The current \(I\) is given as 4.1 kA or \(4.1 \times 10^{3}\) A. The length of the region \(L\) is 1.3 m. The magnetic field \(B\) is 12 T. The angle \(\alpha\) is given as \(60^{\circ}\), but we will need to convert this to radians for our calculations, giving us \(\alpha = \pi / 3\) rad.
02

Calculate the magnetic force

The formula for the magnetic force is given by \(F = I \cdot L \cdot B \cdot \sin \alpha\). Plugging in the given values: \(F = (4.1 \times 10^{3}) A \times 1.3 m \times 12 T \times \sin(\pi/3) rad\). This gives us an approximate force of \(F = 34194.612 N\).
03

Convert the force to pounds

Newton is the SI unit for force. To convert the force from newtons to pounds, use the conversion factor of 0.2248 pounds/newton. So, \(34194.612 N \times 0.2248 lb/N = 7687.546 lb\).
04

Compare the calculated force with 10000 pounds

The calculated force on the bar is 7687.546 lb, which is less than 10000 pounds. Therefore, the claim that the magnetic force will exceed 10000 pounds is not correct.

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Most popular questions from this chapter

A wire \(1.0 \mathrm{mm}\) in diameter carries \(5.0 \mathrm{A}\) distributed uniformly over its cross section. Find the field strength (a) \(0.10 \mathrm{mm}\) from its axis and (b) at the wire's surface.

An electron is moving in a uniform \(0.25-\) T magnetic field; its veIocity components parallel and perpendicular to the field are both 3.1 Mm/s. (a) What's the radius of the electron's spiral path? (b) How far does it move along the field direction in the time it takes to complete a full orbit about the field?

Find an expression for the magnetic field at the center of a square loop of side \(a\) carrying current \(I\)

Three parallel wires of length \(l\) each carry current \(I\) in the same direction. They're positioned at the vertices of an equilateral triangle of side \(a,\) and oriented perpendicular to the triangle. Find an expression for the magnitude of the force on each wire.

A rectangular copper strip measures \(1.0 \mathrm{mm}\) in the direction of a uniform 2.4 -T magnetic field. When the strip carries a \(6.8-\) A current perpendicular to the field, a 1.2 - \(\mu\) V Hall potential develops across the strip. Find the number density of free electrons in the copper.
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