How to Calculate Magnetic Fields from Currents

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  • 0:04 Current Flow
  • 1:18 Right-Hand Rule
  • 1:49 Examples
  • 2:57 Magnetic Field Strength
  • 4:50 Application
  • 5:09 Lesson Summary
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Lesson Transcript
Instructor: Matthew Bergstresser

Matthew has a Master of Arts degree in Physics Education. He has taught high school chemistry and physics for 14 years.

Electric current generates a magnetic field. In this lesson, we'll investigate how to determine the direction of a magnetic field based on current direction and the strength of the field based on the current value and its distance from the wire.

Current Flow

Did you know that when you use your right hand to give the thumbs up or thumbs down sign you're using a physics trick? We call it the right-hand rule, and it's used quite a bit in physics. In this video, we'll use this version of the right-hand rule to determine the orientation of magnetic field generated by current-carrying wires.

Conventional current is the flow of positive charge-carriers and flows from high electrical potential (+) to low electrical potential (-). When current is flowing, magnetic field loops are generated around the wire as shown in this diagram.


Magnetic loops around current-carrying wire
general


Magnetic fields are vectors, so they point in specific directions. With current-carrying wires, the loops are always perpendicular to the current flow. We use arrows to represent the direction of the field, but sometimes the field is pointing into or out of the screen. We use ⊗ to represent ''into the screen'', and • for ''out of the screen.'' Think of these symbols like an arrow. The dot is what the tip of the arrow looks like when viewing it straight on. The ⊗ looks like the fletching of the arrow, which are the vanes or feathers at the opposite end of the tip when viewing it straight on.

Right-Hand Rule

Imagine drawing multiple arrows on the back of your right hand that extend from your wrist to the tip of your pointer finger. Now, take your right hand and make a ''thumbs up'' sign while pretending to grip the wire carrying the current with your thumb pointing in the direction of current flow. The arrows you imagined drawing on the back of your hand point in the direction of the magnetic field around the wire.

Let's go through some examples to determine which way the magnetic field points based on current flow direction.

Examples

Prompt 1: Determine the magnetic field directions at the numbered locations.


ex1


Here's the solution: Pointing your right thumb to the right and curling your fingers around the wire, you can say that there's no magnetic field at points 1 and 3 because there is no electric current at those locations. At location 2, your right fingers come out of the screen, while at location 4 your fingers point into the screen.


Magnetic field in blue
Ex1B

Prompt 2: Determine the magnetic field directions at the numbered locations.


up_current


In the solution, your right thumb points up and your fingers curl around the wire. At location 1, your fingers are coming out of the screen, and at location 2, your fingers point into the screen.


Magnetic field in blue
upcurrent_B


Prompt 3: Determine the magnetic field for the current pointing out of the screen.


current_out


Here's the solution: Your right thumb points out of the screen at yourself, like you're gesturing and saying the words, ''this guy'' or ''this girl.'' Your right fingers point to the left at the top of the wire, downward on the left side of the wire, to the right at the bottom of the wire and up on the right side of the wire.


Magnetic field in blue
Current_outB


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