Chapter 29, Problem 47CP

### Physics for Scientists and Enginee...

10th Edition
Raymond A. Serway + 1 other
ISBN: 9781337553278

Chapter
Section

### Physics for Scientists and Enginee...

10th Edition
Raymond A. Serway + 1 other
ISBN: 9781337553278
Textbook Problem

# A wire carrying a current I is bent into the shape of an exponential spiral, r = eθ, from θ = 0 to θ = 2π as suggested in Figure P29.47. To complete a loop, the ends of the spiral are connected by a straight wire along the x axis. (a) The angle β between a radial line and its tangent line at any point on a curve r = f(θ) is related to the function by tan β = r d r / d θ Use this fact to show that β = π/4. (b) Find the magnetic field at the origin.Figure P29.47

(a)

To determine

To show: The angle β between a radial line and its tangent line at any point on a curve r=f(θ) is π4 .

Explanation

Given info: The value of r=eÎ¸ from Î¸ to 2Ï€ .

Formula to calculate the differentiation of the exponential spring is,

drdÎ¸=d(eÎ¸)dÎ¸=eÎ¸

Write the expression for the angle between a radial line and its tangent line is,

tanÎ²=rdr/dÎ¸

Substitute

(b)

To determine
The magnetic field at origin.

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