Magnetic Fields from Currents

The video lesson for this topic is coming soon.

Essential Question

How can electricity make a magnet?

Magnets are not the only things that make magnetic fields. By the end of this lesson, you should be able to find the direction of the magnetic field around a wire or a coil with the right-hand grip rule and explain how to make an electromagnet stronger.

Oersted’s Discovery

Current in a wire turns a compass
Moving charges make magnetic fields
No current, no field

Two top views of a compass with a wire running north and south over it. Left, switch off: the needle points north. Right, current on and flowing north: the needle swings toward the northwest.

In 1820, Hans Christian Oersted noticed that a compass needle swung when he turned on the current in a nearby wire. When he switched the current off, the needle swung back to point north. This showed that an electric current makes a magnetic field. In fact, any moving charge makes a magnetic field. Charges sitting still do not.

Field Around a Wire

Field lines are circles around the wire
Closer to the wire: stronger
More current: stronger

A wire seen end-on, drawn as a circle with a dot because its current comes out of the page. Three blue circles surround it with arrows going counterclockwise. The gaps between circles grow larger farther from the wire. Caption: current out of the page.

The magnetic field around a long straight wire forms circles centered on the wire. Here the wire points straight out of the page, so we see it end-on, and the current comes toward you. The field is strongest close to the wire and gets weaker farther away, which is why the circles spread apart. More current makes a stronger field.

Dots and Crosses

Dot: out of the page, toward you
Cross: into the page, away from you
Used for both current and field

Left: a circle with a dot, labeled out of the page, like an arrow tip coming at you, above a grid of blue dots labeled B out of page. Right: a circle with an X, labeled into the page, like an arrow's tail going away, above a grid of blue X marks labeled B into page.

Magnetic fields and currents often point straight into or out of the page, which is hard to draw. Physicists use a simple code. A dot means out of the page, toward you, like the tip of an arrow flying at you. A cross (×) means into the page, away from you, like the feathers on the tail of an arrow flying away. A grid of dots shows a magnetic field coming out of the page. A grid of crosses shows a field going into the page.

Right-Hand Grip Rule

Thumb points along current I
Fingers curl the way B circles
I = conventional current (+ flow)

A right hand grips a vertical wire with the thumb pointing up along the red current arrow I. A blue loop around the wire with arrows shows the field circling counterclockwise when viewed from above, the same way the fingers curl.

To find which way the field circles, use the right-hand grip rule. Grab the wire with your right hand so your thumb points in the direction of the current. Your fingers curl around the wire in the direction of the magnetic field. In this unit, current always means conventional current: the direction positive charges would move, from the + side of a battery to the − side. (Electrons actually move the opposite way, but every right-hand rule here uses conventional current.)

Wire in the Page

Field pokes through the page
Current up: × on the right
Current up: • on the left

A vertical wire with a red current arrow pointing up. To the left of the wire is a grid of blue dots, meaning the field points out of the page. To the right is a grid of blue crosses, meaning the field points into the page.

When a wire lies flat in the page, its circular field passes through the page: it comes up out of the page on one side of the wire and goes back down into the page on the other side. For a current pointing up the page, the right-hand grip rule shows the field points into the page (×) on the right of the wire and out of the page (•) on the left.

Field of a Coil

Coil: many loops of wire
Inside, the loops’ fields add up
A coil acts like a bar magnet

A cut-away view of a coil. The top row of wires has dots, meaning current out of the page, and the bottom row has crosses, meaning current into the page. Field lines run straight through the inside from left to right, leave the right end, which is labeled N, and loop around the outside to enter the left end, labeled S.

Wind a wire into a coil (also called a solenoid) and the fields from all the loops add together inside it. This picture slices the coil in half: the top wires carry current out of the page (dots) and the bottom wires carry current into the page (crosses). Inside the coil, the field is strong and points straight along the coil. Outside, the field lines loop around from one end to the other, exactly like a bar magnet. The end where the field lines come out is the N pole. To find it, curl the fingers of your right hand the way the current goes around the loops, and your thumb points to the N end.

Electromagnets

Coil wrapped around an iron core
Current on: magnet. Current off: not
Used in cranes, speakers, and doorbells

An iron nail with copper wire coiled around it. The wire ends connect to a battery below. Several paper clips cling to the tip of the nail.

An electromagnet is a coil of wire wrapped around an iron core, like a nail. When current flows, the coil makes a magnetic field, and the iron’s domains line up with it, making the field much stronger. When the current stops, the field disappears. Because you can switch it on and off, electromagnets are used in scrapyard cranes, speakers, doorbells, MRI machines, and electric motors.

Making It Stronger

B ∝ N × I

B = strength of the magnetic field
N = number of turns (loops) in the coil
I = current, in amperes (A)

A yellow equation box: B is proportional to N times I. Below it, three cards: double the current and the field doubles; double the turns and the field doubles; add an iron core and the field gets much stronger.

For a coil of a given length, the field is proportional to the number of turns times the current. Double the current and the field doubles. Double the turns and the field doubles. Do both and the field is four times as strong. Adding an iron core multiplies the field many times over, because the iron’s domains line up and add their own fields.

Worked Examples

Try each problem on your own first, then check your work against the solution.

Example 1: Field Next to a Wire

A long straight wire carries current toward the bottom of the page. Does the magnetic field at point P, to the left of the wire, point into or out of the page?

A vertical wire with a red current arrow I pointing down. Point P is a black dot to the left of the wire.

Rule: Right-hand grip rule: thumb along the current, fingers curl in the direction of the field.
Thumb: Point your right thumb down the page, along I.
Fingers: Your fingers come out of the page on the right, wrap over the wire, and go down into the page on the left.
Answer: The field at P points into the page (×).

Example 2: Current Out of the Page

A wire carries current straight out of the page. Which way does the magnetic field point at point P, directly above the wire?

A wire seen end-on as a circle with a dot, meaning current out of the page. Point P is a black dot directly above it.

Thumb: Point your right thumb out of the page, toward you, along the current.
Fingers: Your fingers curl counterclockwise around the wire.
At P: P is at the top of a counterclockwise circle. Going counterclockwise, the top of the circle moves to the left.
Answer: The field at P points to the left.

Example 3: Which End Is North?

This cut-away coil has crosses (current into the page) on the top row and dots (current out of the page) on the bottom row. Which end of the coil is its N pole?

A cut-away coil. The top row of wire ends shows crosses for current into the page, and the bottom row shows dots for current out of the page. The left and right ends are labeled left end and right end.

Top wire: Current into the page: point your right thumb into the page. Your fingers curl clockwise, so just below the top wire (inside the coil) the field points left.
Bottom wire: Current out of the page: point your thumb toward you. Your fingers curl counterclockwise, so just above the bottom wire (inside the coil) the field also points left.
Field inside: Both rows agree: the field inside the coil points to the left.
Answer: Field lines come out of the left end, so the left end is the N pole.

Example 4: Stronger Electromagnet

An electromagnet has 100 turns of wire carrying 2.0 A. You rewind it with 300 turns and raise the current to 4.0 A. How many times stronger is its magnetic field?

Knowns: Before: N = 100, I = 2.0 A. After: N = 300, I = 4.0 A.
Relationship: B ∝ N × I, so compare N × I before and after.
Before: 100 × 2.0 = 200
After: 300 × 4.0 = 1,200
Answer: 1,200 ÷ 200 = 6.0 times stronger

Another way to see it: tripling the turns triples the field, and doubling the current doubles it again, so 3 × 2 = 6.

Big Ideas

Moving charges (currents) make magnetic fields
Grip rule: thumb = I, fingers curl = B
• out of page, × into page
Coil = electromagnet: B ∝ N × I, iron core helps

Back to the essential question: electricity makes a magnet because any moving charge, including an electric current, creates a magnetic field. The field circles a straight wire, and a coil of wire acts like a bar magnet, which gets stronger with more current, more turns, and an iron core. Next up, we’ll flip the idea around and see how a magnetic field pushes on moving charges.