1. Starting with the expression for the magnetic field of a long solenoid with height h,...
1. Starting with the expression for the magnetic field of a long solenoid with height h, radius R, and N turns, and ignoring end effects, derive the inductance L of such a solenoid using the relation Vz-LI. 2. Two coaxial loops of wire, of radii a, and a, are parallel to each other and separated by distance r> a, ,a2 along their common axis. The loops carry steady currents of I, and l2, Derive the mutual inductance M of the...
3 The magnetic field inside a toroidal solenoid is not uniform as for the long, straight solenoid. Over the cross-sectional area of the toroid the magnetic field is stronger near the inner HoNI radius of the torus and somewhat weaker near the outer radius according to B(r) 2Tr So we cannot technically use the simple expression P2 = BAfor the flux through one turn of wire. Nevertheless, the textbook uses an approximate constant value for an equivalent uniform magnetic field...
Question 3 A long solenoid with n turns per unit length of current I is wrapped around a cylindrical magnetic core of permeability μ μ0Hm The cylindrical core, extending along the z-axis, has radius α n turns per unit length, current I per turn Magnetic material of μ (a) If the solenoid is considered as infinite in length, it can be shown that the magnetic field, expressed in cylindrical coordinates, is: r> a Apply Ampere's law, using the rectangular path...
Magnetic Field due to a Current (a) What is the dimension of n in the expression for the magnetic field B in a solenoid? (b) Suppose you want to wind a solenoid to create a 100 G field in the interior of a cylinder 10 cm long with a radius 0.5 cm. The wire can carry 500 mA current. How will you do it? (c) What is the inductance of your solenoid in Henrys?
Magnetic Field inside a Very Long Solenoid Learning Goal: To apply Ampère's law to find the magnetic field inside an infinite solenoid. In this problem we will apply Ampère's law, written ?B? (r? )?dl? =?0Iencl, to calculate the magnetic field inside a very long solenoid (only a relatively short segment of the solenoid is shown in the pictures). The segment of the solenoid shown in (Figure 1) has length L, diameter D, and n turns per unit length with each...
Font Paragraph Dyes Q4) (8 Points) A long solenoid with 100 turns has a radius of 0.Im and its length is 0.8m. The curent through the solenoid increases according to the relation l(t)-6t+St. A) Calculate the self-inductance voltage in the solenoid at t-2s. B) What is the induced current if its resistance is 52 C What is the direetion of both induced magnetic field and current in the solenoid 1000000000000001
6. A very long solenoid has a density of coils n turns per unit length. We apply a current I through the solenoid. Use Biot-Savart law to derive the magnetic field in the center of the the solenoid. Verify that it agrees with the result from the Ampere's law. You can approximate the solenoid as infinitely long 6. A very long solenoid has a density of coils n turns per unit length. We apply a current I through the solenoid....
Problem 5. (4 points) Electric field induced by a changing magnetic field in a solenoid. long solenoid of radius R = 10 cm has n = 100 turns/cm and carries a time-varying current that varies sinusoidally as I- Imax cos (2rft), where Imax- 10 A is the maximum current and f-60 Hz is the frequency of the alternating current source. What is the maximum magnitude of the induced electric field inside the solenoid, a distance r- 1.3 cm from its...
The magnetic field inside a toroidal solenoid is discussed in Example 28.11 of the text book. There the thickness of the solenoid and variation of the magnetic field across the cross section were ignored. Let's include these effects into consideration. The solenoid in the figure has a rectangular cross section. It has N uniformly spaced turns, with air inside. The magnetic field at a point inside the toroid was derived in Example 28.11. Do not assume the field to be...
Two other systems commonly used in the labs are solenoid and toroid. Use Maxwell laws derive formulas for the magnetic field H inside and outside a) an infinitely long solenoid with radius r and n turns per unit lenght b) toroidal coil with inner radius r1, outer radius r2 and N turns c) Is the field uniform inside the toroid