Unit 7: Magnetic Forces and Fields
A field that pushes only on moving charges, bends them into circles, twists current loops, and sorts positive carriers from negative ones inside a metal strip.
9 topics · 34 questions
Each topic is a path, not a menu: work down it in order and every question builds on the one above. Click any of them to watch the answer draw itself.
What a Magnetic Field Does
- How it worksHow do magnetic field lines emerging from a north pole and curling into a south pole describe a field everywhere?
- Common mistakeWhy can't you ever find just a north pole or just a south pole sitting on its own?
- Going furtherWhat happens to a compass needle's direction as you carry it in a full loop around a bar magnet?
Your turn1 of 2
You cut a bar magnet in half, hoping to isolate a lone north pole. What do you get instead?The Magnetic Force on a Moving Charge
- How it worksHow do a charge's velocity and a field's direction combine through a cross product to set the force's direction?
- Worked exampleFind the magnetic force on a proton moving at 3 times 10 to the 6 m/s perpendicular to a 0.5 tesla field.
- Common mistakeWhy doesn't the magnetic force on a moving charge ever speed that charge up or slow it down?
- Going furtherWhat happens to the magnetic force on a charge as the angle between its velocity and the field shrinks to zero?
- Worked exampleFind the magnetic force on an electron moving at 5 times 10 to the 5 m/s at 30 degrees to a 0.2 tesla field.
Your turn1 of 2
Find the magnetic force on a proton moving at 7 times 106 m/s perpendicular to a 6 times 0.1 tesla field. Use e = 1.602x10−19 C.Circular Motion in a Magnetic Field
- How it worksHow does a magnetic force that's always perpendicular to the velocity bend a straight path into a perfect circle?
- Worked exampleFind the radius of the circular path of an electron moving at 2 times 10 to the 6 m/s in a 0.01 tesla field.
- How it worksWalk me through what changes about a charged particle's path when it enters a field at an angle instead of straight-on.
- Going furtherWhat happens to the radius of a charged particle's circular path if its speed through the field is doubled?
Your turn1 of 2
Find the radius of the circular path of an electron moving at 7 times 106 m/s in a 6 times 0.01 tesla field. Use electron mass m = 9.11x10−31 kg and e = 1.602x10−19 C.Velocity Selectors and Mass Spectrometers
- How it worksHow do the electric and magnetic forces on a charged particle balance each other in a velocity selector?
- Worked exampleFind the speed selected by a velocity selector with a 2000 N/C electric field and a 0.1 tesla magnetic field.
- How it worksWalk me through how a mass spectrometer bends speed-selected ions by mass once a magnetic field takes over.
- Ties togetherHow does the radius formula from a charge's circular motion become the working principle of a mass spectrometer?
Your turn1 of 2
Find the speed selected by a velocity selector with a 3634 N/C electric field and a 6 times 0.1 tesla magnetic field.The Magnetic Force on a Current-Carrying Wire
- How it worksHow does the force on a whole wire come from adding up the magnetic force on every moving charge inside it?
- Worked exampleFind the force on a 0.5 meter wire carrying 4 amps placed perpendicular to a 0.3 tesla field.
- Common mistakeWhy doesn't a current-carrying wire feel any magnetic force at all when it runs parallel to the field?
Your turn1 of 2
Find the force on a 142 cm wire carrying 13 amps placed perpendicular to a 8 times 0.1 tesla field.Force and Torque on a Current Loop
- How it worksHow do opposite forces on opposite sides of a current loop combine into a net torque instead of a net force?
- Worked exampleFind the maximum torque on a square loop of side 5 cm carrying 2 amps in a 0.4 tesla field.
- Common mistakeWhy doesn't a current loop sitting in a perfectly uniform magnetic field ever feel a net sideways force?
- Going furtherWhat happens to the torque on a current loop as it rotates from face-on to edge-on relative to the field?
- How it worksHow does the torque on a current loop reach its maximum value exactly when the loop's face lies parallel to the field?
Your turn1 of 2
Find the maximum torque on a square loop of side 11 cm carrying 13 amps in a 8 times 0.1 tesla field.The Magnetic Dipole Moment
- How it worksHow does a loop's current and enclosed area combine into a single magnetic dipole moment?
- Worked exampleFind the magnetic dipole moment of a circular loop of radius 4 cm carrying a current of 3 amps.
- Ties togetherHow does the torque on a magnetic dipole in a field mirror the torque on an electric dipole in a field?
Your turn1 of 2
Find the magnetic dipole moment of a circular loop of radius 11 cm carrying a current of 13 amps.The Hall Effect
- How it worksHow does the magnetic force on drifting charge carriers pile them up on one side of a conductor until it balances?
- Worked exampleFind the Hall voltage across a 2 mm wide strip carrying 5 amps in a 0.8 tesla field with a carrier density of 8 times 10 to the 28 per cubic meter.
- Common mistakeWhy does the sign of the Hall voltage flip depending on whether the moving carriers are electrons or positive holes?
- Going furtherWhat happens to the size of the Hall voltage as the magnetic field applied to the strip is made stronger?
Your turn1 of 2
Find the Hall voltage across a 4 mm wide strip carrying 13 amps in a 8 times 0.1 tesla field with a carrier density of 6 times 1028 per cubic meter. Use e = 1.602x10−19 C.Applications of Magnetic Force
- How it worksHow does a commutator flip a motor loop's current at just the right moment to keep its torque going one way?
- How it worksWalk me through how a cyclotron uses a magnetic field to spiral particles while an electric field speeds them up.
- Ties togetherHow does the torque on a current loop from a magnetic force become the working principle of every electric motor?
Your turn1 of 2
A simple DC motor's current loop would only rotate partway and then oscillate back and forth, if not for one key component. What does a commutator do to keep it spinning continuously in one direction?