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Understanding Magnetic Field Strength: Wire, Loop, and Solenoid Calculations

This guide explores the magnetic field strength generated around a wire, inside a loop, and within a solenoid. It explains key principles, such as the direct relationship between current (I) and magnetic field strength (B), as well as the inverse relationship with distance (r). Additionally, mathematical formulas for each scenario are provided, including the equations for a single loop and a solenoid, showcasing how to calculate the magnetic field strength with practical examples. This overview is essential for students of physics and electrical engineering.

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Understanding Magnetic Field Strength: Wire, Loop, and Solenoid Calculations

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Presentation Transcript

  1. Magnetic Field Strength Around a Wire

  2. From the demonstration, we saw that: • the magnetic field strength varies directly with the amount of current flowing through the wire • i.e. B  I • the magnetic field strength varies inversely with the distance from the wire. • i.e.

  3. Thus we combine these together to get • as an equation • for mathematical & historical reasons the constant k has been written as

  4. however we shall for simplicity use "k“ • Our formula then is • where B = magnetic field strength (Tesla) • I = current (Amps) • r = distance from wire (m) • k = permeability of free space constant = 2 x 10 -7

  5. Sample: A vertical wire carries a current of 25.0 A. What is the magnetic field strength 15 cm from the wire?

  6. Magnetic Field Strength inside a Loop • We predict the field strength will be greater inside a loop. There are wires all around the region exerting a magnetic field. The lines of flux reinforce each other. The formula for a single loop is r = radius of coil

  7. For a coil, the strength depends on the number of coils. (N)

  8. Sample: If the magnetic field strength at the centre of a loop of 12 coils is 4.00 x 10-4 T, and the radius is 12.0 cm, find the current that is flowing,

  9. Magnetic Field Strength inside a Solenoid • The formula for magnetic field strength inside a solenoid is • B = 2knI where n = number of turns / m

  10. Sample: A 10 cm long solenoid has 400 turns of wire and carries a current of 2.00 A. Calculate the magnetic field strength inside the solenoid. n = 400 turns / 0.1m = 4000 / m B = 2knI B = 22 x 10-7(4000)(2) B=1.0 x 10-2 T

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