Unit 4 day 2 – Forces on Currents & Charges in Magnetic Fields (B)
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Transcript of Unit 4 day 2 – Forces on Currents & Charges in Magnetic Fields (B)
Unit 4 day 2 – Forces on Currents & Charges in Magnetic Fields (B)
• The force exerted on a current carrying conductor by a B-Field
• The Magnetic Force on a Semi-Circular Wire
• Force on an Electric Charge Moving through a B-Field
• Path of an Electric in a B-Field
• A Particle traveling in both an E- & B-Field
The Force Exerted on a Current Carrying Conductor in a B-Field
#2
• Not only does a current in a wire generate a magnetic field and exert a force on a compass needle, but by Newton’s 3rd Law, the reverse is also true. A magnet can also exert a force on a current carrying conductor
Magnetic Force on a Current Carrying Conductor
where l is the length of wire immersed in the magnetic field
• This implies that the direction of the force is perpendicular to the direction of the B-Field (Right Hand Rule #2)
• Then the maximum force is:
BlIF
IlBF
Magnetic Force on a Current Carrying Conductor
• If the direction of the current is not perpendicular to the B-Field, but rather at some angle θ then:
sinIlBBlIF
Magnetic Force on a Current Carrying Conductor
• The equation assumes the magnetic fields is uniform & the current carrying conductor does not make the same angle θ with B
• SI Units for B-Field is Tesla (T) 1 T = 1N/A-m
• We can explore the above equation in differential form:
where dF is the infinitesimal force acting on a differential length dl of the wire
BlIF
BlIdFd
Magnetic Force on a Semi-Circular Wire
IBRF 2
Force on an Electric Charge Moving Through a B-Field
where Δt is the time for charge q to travel a distance l
or the force on a particle is:
tvlandtNqIwhereBlIF
BtvtNqF
BvqF
Force on an Electric Charge Moving Through a B-Field
• If , then the force is a maximum and
• If the velocity is at some angle θ wrt the B-Field, then:
Bv qvBF max
sinqvBF
Path of an Electron in a Magnetic Field
• If , then the electron will move in a curved circular path, and the magnetic force acting on it will act like a centripetal force
• The radius of the circular orbit will be:
• The period for 1 revolution will be:
• The Cyclotron Frequency is:
Bv
Bqvmr
e
e
BqmTe
e2
e
e
mBq
Tf
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Path of an Electron in a Magnetic Field
• Note: if the Particle was a proton, the circular path would be upward (counter-clockwise)
A Particle Traveling in Both an E- & B- Field
• The force on a particle traveling in the presence of both an electric and magnetic field which are mutually perpendicular, is given by the Lorentz Equation:
• For a particle to travel straight through, the net force on the particle must equal zero, yielding a velocity selector:
BEv
BvEqF