Magnetic Field Induced Current

In summary, the conversation discusses finding the rate at which the magnitude of a uniform magnetic field needs to change in order to induce a 10 A current in a circular loop made of wire with given dimensions and resistivity. The solution involves finding the EMF using the formula ε=IR and then using it to find the rate of change of the magnetic field, dB/dt. It is important to pay attention to units and use the correct value for the radius of the wire.
  • #1

Homework Statement

A uniform magnetic field
is perpendicular to the plane of a circular loop of diameter 18 cm formed from wire of diameter5.0 mm and resistivity 1.69 ✕ 10−8 Ω · m. At what rate must the magnitude of
change to induce a 10 A current in the loop

Homework Equations

Φ = ∫ B ⋅ dA (in vector form)
φ= BA
ε= -dΦ/dt
R= ρL/A

The Attempt at a Solution

Current is given, so I fould the Emf using ε=IR
ε= (10) x ((1.69E-8)(2π⋅0.09))/(π⋅0.0052)) = 0.001217

Then using the value obtained for ε,
0.001217 = dΦ/dt

0.001217⋅A = dB/dt

wouldn't dB/dT be the rate that B is changing?
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  • #2
PhysicsInNJ said:
wouldn't dB/dT be the rate that B is changing?
It is, but the units are not Ampere. In general, working with units helps to find most errors.
Be careful with diameter and radius of the wire.
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  • #3
Oh I see, my mistake was actually I used diameter instead of radius. Thank you!

1. What is a magnetic field?

A magnetic field is a region in space where a magnetic force can be detected. It is created by moving electric charges, such as electrons, and is characterized by its direction and strength.

2. How is a magnetic field induced current created?

A magnetic field induced current is created when a conductor, such as a wire, is placed in a changing magnetic field. The moving magnetic field induces a flow of electrons in the conductor, creating an electric current.

3. What is the relationship between the magnetic field and the induced current?

The strength of the induced current is directly proportional to the strength of the magnetic field and the rate of change of the magnetic field. A stronger magnetic field or a faster changing magnetic field will result in a stronger induced current.

4. How is the direction of the induced current determined?

The direction of the induced current is determined by the direction of the changing magnetic field. This is known as Lenz's law, which states that the induced current will flow in a direction that opposes the change in the magnetic field.

5. What are some practical applications of magnetic field induced current?

Magnetic field induced current has many practical applications, including generators, transformers, and electric motors. It is also used in technologies such as magnetic levitation and magnetic resonance imaging (MRI) machines.