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Chapter 29: Problem 59

A 100 -turn solenoid of length \(8 \mathrm{~cm}\) and radius \(6 \mathrm{~mm}\) carries a current of 0.4 A from right to left. The current is then reversed so that it flows from left to right. By how much does the energy stored in the magnetic field inside the solenoid change?

Short Answer

Expert verified
Answer: The change in energy stored in the magnetic field inside the solenoid after the current is reversed is zero.

Step by step solution

01

Calculate the cross-sectional area of the solenoid

We are given the radius of the solenoid (\(r = 6 \mathrm{mm}\)). To find the cross-sectional area \((A)\), we'll use the formula: \(A = \pi r^2\) Once we have the area, we will use it to determine the inductance of the solenoid.
02

Calculate the inductance of the solenoid

With the cross-sectional area calculated, we can now determine the inductance (\(L\)) of the solenoid using the formula: \(L = \dfrac{\mu_0 N^2 A}{l}\) We are given all other necessary values: \(N = 100\) \(l = 8 \mathrm{cm} = 0.08 \mathrm{m}\) \(\mu_0 = 4\pi \times 10^{-7} \mathrm{T\cdot m/A}\)
03

Calculate the energy stored in the magnetic field before and after the current reversal

We will now calculate the energy stored in the magnetic field (\(U\)) before and after the current reversal using the inductance (\(L\)) we calculated in step 2 and the given current values (\(I\)). Since the magnitude of the current is the same before and after the reversal, the energy stored in the magnetic field for both cases will be the same: \(U_1 = U_2 = \dfrac{1}{2}L I^2\) Where: \(U_1\) - Energy stored before the current reversal \(U_2\) - Energy stored after the current reversal
04

Calculate the change in energy stored in the magnetic field

Finally, we can find the change in energy stored in the magnetic field by finding the difference between the energy stored before and after the current reversal: \(\Delta U = |U_2 - U_1|\) Since both energies are equal, the change in energy stored in the magnetic field is zero.

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Most popular questions from this chapter

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