How Do You Calculate Magnetic Field Magnitude for a Specific Flux?

In summary, the flux through a horizontal surface in a uniform magnetic field directed at an angle of 34.5∘ above the horizontal should be 0.84T.
  • #1
Yosty22
185
4

Homework Statement



A horizontal rectangular surface has dimensions 3.10cm by 3.05cm and is in a uniform magnetic field that is directed at an angle of 34.5∘ above the horizontal. What must the magnitude of the magnetic field be in order to produce a flux of 4.5E-4 Wb through the surface?

Homework Equations



Magnetic Flux = BAcos(θ)

The Attempt at a Solution



Using the above equation, I solved for B, getting B=Flux/Acos(θ)
I then plugged in my numbers: (4.5*10^-4)/((.0305)(.031)cos(34.5)) and got that B should equal 0.5775T. However, it says the answer is wrong, any ideas what I did wrong?
 
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  • #2
I'd suggest that you make a sketch. You're looking for the flux through a horizontal surface, which means you want the vertical component of the B field...

Alternatively, take a vector equation approach and construct vectors for B and the area normal, then expand

##\Phi = \vec{B}\cdot (A\vec{n})##
 
  • #3
So how do I go about finding that, though? I understand that I need the vertical component, but I have no idea how to set it up if all I know is the angle?
 
  • #4
Yosty22 said:
So how do I go about finding that, though? I understand that I need the vertical component, but I have no idea how to set it up if all I know is the angle?

Make a sketch! Draw a horizontal line to show your area of interest in profile. Draw a vector or two representing the B field. What angle do you need? You can also choose the appropriate trig function and use the angle as given.

attachment.php?attachmentid=62662&stc=1&d=1381328892.gif


You want the component of B that's parallel to the surface normal of your area.
 

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  • #5
Okay, so I would say that B_n (normal component of the B field) = Bsin(34.5), then I can do the flux divided by sin(34.5) times the area, so I have B=4.5*10^-4/((sin34.5)(.031)(.0305)). That way I get B=0.84?
 
  • #6
Yosty22 said:
Okay, so I would say that B_n (normal component of the B field) = Bsin(34.5), then I can do the flux divided by sin(34.5) times the area, so I have B=4.5*10^-4/((sin34.5)(.031)(.0305)). That way I get B=0.84?

Sure. Add the appropriate units and you're good.
 

What is magnetic flux and how is it measured?

Magnetic flux refers to the amount of magnetic field passing through a given surface area. It is measured in units of Weber (Wb) or Tesla meter squared (Tm²). It can be calculated by multiplying the magnetic field strength (in Tesla) by the area (in meters squared) perpendicular to the field.

What factors affect the magnitude of magnetic flux?

The magnitude of magnetic flux is affected by the strength of the magnetic field, the angle between the field and the surface area, and the size of the surface area. The greater the strength of the magnetic field and the larger the surface area, the greater the magnetic flux will be. Additionally, the angle between the field and the surface area affects the amount of flux passing through the area.

What is the difference between magnetic flux and magnetic flux density?

Magnetic flux density (also known as magnetic field strength) refers to the strength of the magnetic field at a specific point. It is measured in units of Tesla (T). Magnetic flux, on the other hand, refers to the total amount of magnetic field passing through a given surface area and is measured in units of Weber (Wb) or Tesla meter squared (Tm²).

How is magnetic flux related to electromagnetic induction?

Electromagnetic induction is the process of generating an electric current in a conductor by moving it through a magnetic field or changing the magnetic field passing through the conductor. The magnitude of the induced current is directly related to the rate of change of magnetic flux passing through the conductor. This relationship is described by Faraday's Law of Induction.

How is magnetic flux used in everyday life?

Magnetic flux is used in a variety of everyday applications, such as in generators to produce electricity, in electric motors to convert electrical energy into motion, and in magnetic sensors used in navigation systems. It is also used in medical imaging techniques such as MRI scans, which use magnetic flux to create detailed images of the body's internal structures.

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