Download Magnetic Field on a Moving Charge

Notes: Magnetism
Dipoles
A dipole is anything that has two opposing sides- positive/negative, north/south. Magnets only come in dipoles.
Don’t get confused- we aren’t talking about positive and negative charges when we talk about magnets- we are talking
about north and south poles- and one cannot exist without the other (except in super rare cases, which we won’t discuss now, and might
get to in quantum, fingers crossed)
North poles are attracted to south poles and repelled by other north poles. The reverse is also true.
Drawing Magnetic Field Lines
Magnetic field lines show the direction a small magnet would point at any given position on
or near a magnet.
We use a capital B for magnetic field strength. You will often see it bolded or with a little
arrow for a hat because it is a vector.
We measure magnetic field strength in Teslas (T)
Practice: Draw the magnetic field lines
Electricity and Magnetism
Key Idea: When you have a moving charge, you create a magnetic field around it.
Let’s say we had a line of moving charges (in other words, a current). What type of magnetic field look like around it?
We can figure it out using the right hand rule.
The thumb points in the direction of the current. The direction of your fingers shows
the curve the field lines make.
Practice: Draw the Magnetic Field Lines for the following wires
AP Practice: Compass near a wire
A long straight wire conductor is placed below a compass as shown in the top view figure.
When a large conventional current flows in the conductor as shown, the N pole of the
compass:
A) remains undeflected B) points to the south
C) points to the west D) points to the east E) has its polarity reversed
Solenoids
What if we had a wire in a loop? What would that magnetic field look like?
A solenoid is made by stacking loops of wire on top of each other to create a strong magnetic field through the center.
AP Practice: Field Outside a solenoid
A compass is placed near a coil of wire. A conventional electrical
current is then run through the coil from left to right as shown. This
will cause the North pole of the compass to:
A) point toward the left
B) point toward the right
C) point toward the bottom of the paper
D) not move since the magnetic field of the coil is into the paper
E) not move since the magnetic field of the coil is out of the paper
Magnetic Force on a Current
What happens if we have a current (wire) going through a magnetic field?
⃗⃗
𝐹𝐵 = 𝐼 𝑙⃗ × 𝐵
𝐹𝐵 = 𝐼𝑙𝐵𝑠𝑖𝑛𝜃
where the angle is the angle between l and B
Practice: Example Problem
Imagine a wire (current= 3A, length= 0.2m) is passing through a magnetic force with a strength of 2 T. Find the force on
the wire.
The Second Right Hand Rule
Magnetic Field on a Moving Charge
What happens to a charge moving through a magnetic field?
⃗⃗ or 𝐹 = 𝑞𝑣𝐵𝑠𝑖𝑛𝜃
𝐹⃗ = 𝑞𝑣⃗ × 𝐵
Derivation:
What path does a proton take through a magnetic field?
Remember this blast from the past?
𝐹𝑐 =
𝑚𝑣 2
𝑟
Does it take any work to keep this charge moving?
AP Practice: Particle in a Magnetic Field
An ion with charge q, mass m, and speed V enters a magnetic field B and is deflected into a path with a radius
of curvature R. If a second ion has speed 2V, while m, q, and B are unchanged, what will be the radius of the
second ion’s path?
A) 4R B) 2R C) R D) R/2 E) R/4
2007B2: Mass Spectrometer
(a) In what direction must B point to produce the trajectory of the ions shown?
(b) The ions travel at constant speed around the semicircular path. Explain why the speed remains constant.
(c) Calculate the speed of the ions with charge +2e that exit at distance x.
(d) Calculate the accelerating voltage E needed for the ions with charge +2e to attain the speed you calculated
in part (c).
Dealing with Negative Charges
You need to flip the current. Remember- current is the path of positive charges. For the right hand rule to work, you
need to realize that electrons move in the opposite direction of the current. Therefore, everything flips.
AP Practice: Negative Charges
An electric current flows through a horizontal wire as shown. Which option best represents the direction of the magnetic field
at point P
A) into the page
B) out of the page
C) to the right of the page
D) toward the top of the page
E) toward the bottom of the page
AP Practice: Wire Moved through Field
A wire moves with a velocity v through a magnetic field and
experiences an induced charge separation as shown. What is the
direction of the magnetic field?
A) into the page
B) towards the bottom of the page
C) towards the right
D) out of the page
E) towards the top of the page