Magnetic Field and Flux AP Problem

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Magnetic Field and Flux AP Problem 

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Electromagnetism AP Problem 

× X X X X 

× 

× 

× 

, East

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y 

Motional emf AP Problem 

View from above 

Due Date: 

X "= O 

A r~l gun is a de~4ce dial propels aprojectile using a magnetic force, A si~lified diagrmn of ttfis device is 

shown above. The proje~fe in the picture is a ~m’ of mass M and length D, which has a cortstant curt’eat 1 

flowing throuNl it in the +.y-dlrecdon, as sho,a~a. The space between the thin frictionless rails contains a uNform 

magnetic field B, peipendicular to the plane of the page. The magnetic field andrails extend for a distance 

The magnetic field exerts a constant force F on the p~oject’~le, as 

Express all algebraic answers to the following parts in terms of the magnitude F of die constant magnetic fo~.ce, 

other quantities givegi above, and fundamental con~tants. 

(a) Determine the position x of the projectile as a function of time t Mille it is on the rail if the projectile starts 

from rest at x = 0 when t = 0, 

(b) Dctemfine the speed of the projectile as it leaves the right-hand end of the track. 

(c) Det~mine the energy supplied to the projectile by the rail gun. 

(d) In what direction must the magnetic field B point in order to create t_he force F Explain your reasoning. 

(e) Calculate the ,*pe~ of the bar when it reache.~ the erM of the tall gi’~’ea the following values. 

B=5T L=10m I=200A M=0.5 kg D= 10era

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g (into page) 

X 

x × x J × 

I 0,20 m 

x ~x xl x 

,---0.20 m-~ 

A squat~ loop of wire of side 0.20 m has a torn reMstance of 0~ ~, ~e l~p is positioned in a uNfo~ 

mag~tie field B ~" 0,030 T. ~e field is dtreOed into t~ pag~ p~pendi~la m the plane 6fthe Ioop~ as 

(a) Caleulalelhe m~nefie flux O tN’ough ~e 

~e fidd s~ng~ now in~e~s~ uNf~mly to 0.~ T in 0.50 s. 

(b) Calculate the emf &* indue~ in the loop dt~i~ N this 

L Cal~:late ~e m~Ntude I oflhe c~rent in ~e I~p during ~s ~ri~ 

iL What is the Nrmtion of~e mnent in the laop 

Cloc~dse 

C~nterclo~wise 

Justi~ }~ ~swer. 

(d) Descfi~ a me~od by Milch you c~ld i~uce a c~nt in t~e loop if t~ magnetic field remain~

Due Date: 

Electromagnetic Induction AP Problem 

Position I Position 2 

o o 

B out of page 

B equal to zero 

A 20-turn wire coil in the shape of a rectangle, 0.25 In by 0.15 In, has a resistance of 5.0 ~). In position 1 shown 

above,-the.loop is in a uniform magnetic field B of 0.20 T. The field is directed out of the page, perpendicular to 

the plane of the loop. The loop is pulled to the right at a constant velocity, reaching position 2 in 0.50 s. xvhere B 

is equal to zero. 

(a) Calculate the average emf induced in the 20-turn coil during this period. 

(b) Calculate the Inagnitude of the current induced in the 20-turn coil an~d state its direction. 

(c) Calculate the power dissipated in the 20-turn coil. 

(d) Calculate the Inagnitude of the average force necessary to reinove the 20-turn coil fmin the Inagnetic field. 

(e) Identical wire is used to add 20 Inore turns of wire to the original coil. How does this affect the current in 

the coil Justify yottr answer.

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Tap view

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Region ~ Region 11 

Particle x x 

x x x x 

A beara of particles of charge q = -~:3.2 x t0 -t~ C andmass m = 6,68 x lO -u~ kg enters region I with a range 

of velocities all in the direction show~ in the diagram above. The~ is a magnetic field in region I directed into 

the page with magnitude B = 0.12 T. Charged metal plates are placed in appropriate locations to create a uniform 

electric field of magnitude E = 4800 NiC in region L As a re~t, some of the charged garticles pass swaight 

through region I tmdeflected. Gravitational effects are negligible. 

i. On the diagram above, Sketch electric field lines in region I. 

Calculate,the spe~ of the particles that pa_~s straight through region I. 

The particles that pass stmi~at through enter region 1I in which there is no electric field artd the magnetic field 

has the same magnitude and direction as in region L The path of t~e particles in region 1t is a circular ate of 

radius!/. 

(b) Calculate the radius R. 

(e) Within the beam there are particles mo\4ag flower than the speed you calculated in (aXL In what direction 

is the net initial force on these particles as they enter region I 

__ To the left Toward the top of the page __Out~the#aneof~epage 

__ To the right __ Toward the bottom ofthe page __ Into the plane of the page 

(d) A pinkie of the same ma~ and the same speed as in (a)il but with cha~ge q = -3 2 × 10-19 C enters 

region I. On ~ follo~,iag diagram, sketch the complete resulting path of the ac~icle. 

X × × X 

Region 11 

x x B×

2009 AP ® PHYSICS B FREE-RESPONSE QUESTIONS 

Metal Rod 

~~0 T x x X 

X 

X 

1.8 rods 

3.0~: 

0.52 m 

× × 

X 

x 

String 

x 

X 

0.20 

Top View 

A metal rod of mass 0.22 kg lies across two parallel conducting rails that are a distance of 0.52 m apart on a 

tabletop, as shown in the top view above. A 3.0 ~2 resistor is connected across the left ends of the rails. The 

rod and rails have negligible resistance but significant friction with a coefficient of kinetic friction of 0.20. 

There is a magnetic field of 0.80 T perpendicular to the plane of the tabletop. A string pulls the metal rod to 

the right with a constant speed of 1.8 m/s. 

(a) Calculate the magnitude of the current induced in the loop formed by the rod, the rails, and the resistor. 

(b) Calculate the magnitude of the force required to pull the rod to the right with constant speed. 

(c) Calculate the energy dissipated in the resistor in 2.0 s. 

(d) Calculate the work done by the string pulling the rod in 2.0 s. 

(e) Compare your answers to parts (c) and (d). Provide a physical explanation for why they are equal or 

unequal. 

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rectangular wire loop is connected across a power supply with an internal resistance of 0.50 ~ and an emf 

of 16 V. The wire has resistivity 1.7 x 10 -8 ~om and cross-sectional area 3.5 x 10 .9 m 2 . When the power 

supply is turned on, the current in the wire is 4.0 A. 

(a) Calculate the length of wire used to make the loop. 

The wire loop is then used in an experiment to measure the strength of the magnetic field between the poles of 

a magnet. The magnet is placed on a digital balance, and the wire loop is held fixed between the poles of the 

magnet, as shown below. The 0.020 m long horizontal segment of the loop is midway between the poles and 

perpendicular to the direction of the magnetic field. The power supply in the loop is turned on, so that the 4.0 A 

current is in the direction shown. 

Balance 

Note: Figure not drawn to scale. 

(b) In which direction is the force on the ~ due to the current in the wire segment 

__Upward 

Downward 

Justify your answer. 

(c) The reading on the balance changed by 0.060 N when the power supply was turned on. Calculate the 

strength of the magnetic field. 


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Suppose that various rectangular loops with the same total length of wire as found in part (a) were constructed 

such that the lengths of the horizontal segments of the wire loops varied between 0.02 in and 0.10 m. The 

horizontal segment of each loop was always centered between the poles, and the current in each loop was always 

4.0 A. The following graph represents the theoretical relationship between the magnitude of the force on the 

magnet and the length of the wire. 

0.35 

0.30 

0.25 

0.20 

0.15 

O. 10 

0.05 

0,00 

0.00 j 

0.02 0.04 0.06 0.08 0.10 0.12 

Length (meters) 

(d) On the graph above, sketch a possible relationship between the magnitude of the force on the magnet and the 

length of the wire segment if the wire segments were misaligned and placed at a constant nonperpendicular 

angle to the magnetic field, as shown below. 

(e) Suppose the loops are correctly placed perpendicular to the field and the following data are obtained. 

Describe a likely cause of the discrepancy between the data and the theoretical relationship. 

0,35 

0.30 

~0.25 

0.20 

0.15 

0.10 

0.05 

0.00 0.00 0.02 0.04 0.06 0.08 0.10 0.12 

Length (meters) 


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2009 AP ® PHYSICS B FREE-RESPONSE QUESTIONS (Form B) 

y (m) 

qA 

qB 

qB 

-0.040 -0.020 0 0.020 0.040 

Three particles are arranged on coordinate axes as shown above. Particle A has charge qA = -0.20 nC, and is 

initially on the y-axis at y = 0.030 m. The other two particles each have charge qB = +0.30 nC and are held 

fixed on the x-axis at x = -0.040 m and x = +0.040 m, respectively. 

(a) Calculate the m_~ggnitude of the net electric force on particle A when it is at y = 0.030 m, and state 

its d’~. 

(b) Particle A is then released from rest. Qualitatively describe its motion over a long time. 

In another experiment, particle A of charge qA = --0.20 nC is injected into a uniform magnetic field of strength 

0.50 T directed into the page, as shown below, entering the field with speed 6000 m/s. 

X X X X X X X X 

X 

X 


X 

X 


X 

X 

Region of 



X 

X 

~ Magnetic Field 

(c) On the diagram above, sketch a complete path of particle A as it moves in the magnetic field. 

(d) Calculate the magnitude of the force the magnetic field exerts on particle A as it enters the magneric field. 

(e) An electric field can be applied to keep particle A moving in a straight line through the magnetic field. 

Calculate the ~ of this electric field and state its direction. 


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(Current into the page) 

North 

I~) -Probe West+East 

1- d "l South 

A student is measuring the magnetic field generated by a long, straight wire carrying a constant current. A 

magnetic field probe is held at various distances d from the wire, as shown above, and the magnetic field is 

measured. The graph below shows the five data points the student measured and a best-fit curve for the data. 

Unfortunately, the student forgot about Earth’s magnetic field, which has a value of 5.0 x 10 -5 T at this 

location and is directed north. 

10.09.0 

~" 8.0 

7.0 

6.0 

~ 5.0 

"= 4.0 

3.0 

2,0 

1.0 

O 

0.01 0.02 0.03 0.04 0.05 0.06 

Distance (m) 

0.07 0.08 0.09 

(a) On the graph, plot new points for the field due only to the wire. 

(b) Calculate the value of the current in the wire. 


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2008 AP ® PHYSICS ]~ FREE-RESPONSE QUESTIONS (Form B) 

Another student, who does not have a magnetic field probe, uses a compass and the known value of Earth’s 

magnetic field to determine the magnetic field generated by the wire. With the current turned off, the student 

places the compass 0.040 m from the wire, and the compass points directly toward the wire as shown below. The 

student then turns on a 35 A current directed into the page. 

Wire (no currenO 

T 0 

0.040 m 

North 

West + East 

Compass 

South 

Note: Figure not drawn to scale. 

(c) On the compass, sketch the general direction the needle points after the current is established. 

(d) Calculate how many degrees the compass needle rotates from its initial position pointing directly north. 

The wire is part of a circuit containing a power source with an emf of 120 V and negligible internal resistance. 

(e) Calculate the total resistance of the circuit. 

(f) Calculate the rate at which energy is dissipated in the circuit. 


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~-0.20 m-,~ X X X X X X X 

2.0 T 

X X X X X X X 

X X X X X X X 

0 0.10 0.20 0.30 0.40 0.50 0.60 

, x (m) 

The plastic cart shown in the figure above has mass 2.5 kg and moves with negligible friction on a horizontal 

surface. Attached to the cart is a rigid rectangular loop of wire that is 0A0 m by 0.20 m, has resistance 4.0 ~, 

and has a mass that is negligible compared to the mass of the cart. The plane of the rectangular loop is parallel to 

the plane of the page. A uniform magnetic field of 2.0 T, perpendicular to and directed into the plane of the page, 

starts at x = 0, as shown above. 

(a) On the figure below, indicate the direction of the induced current in the loop when its front edge is at 

x = 0.12 m. 

Justify your answer. 

(b) When the front edge of the rectangular loop is at x = 0.12 m, its speed is 3.0 m/s. Calculate the following 

for that instant. 

i. The magnitude of the induced current in the rectangular loop of wire 

ii. The magnitude of the net force on the loop 

(c) At a later time, the cart and loop are completely inside the magnetic field. Determine the magnitude of the 

net force on the loop at that time. Justify your answer. 

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2011 AP e PHYSICS B FREE-RESPONSE QUESTIONS (Form B) 

Radioactive 

Source 

Region 1 

The diagram above illustrates a velocity selector, labeled region 1. It consists of two parallel conducting 

plates, with charges on the plates as indicated creating an electric field of magnitude E directed toward the 

top of the page. A uniform magnetic field of magnitude B 1 directed out of the page exists between the plates. 

The magnitude of the magnetic field can be adjusted so that only particles of a particular speed pass through the 

selector in a straight line. A radioactive source to the left of the selector emits charged particles, each having the 

same charge +q and moving to the right in the plane of the page. The effect of gravity can be neglected 

throughout the problem. 

(a) 

i. Derive the equation v = E/BI for the speed v of particles that move in a straight line through 

region 1. 

ii. Some particles are emitted from the source with speeds greater than E/B~. Which of the following 

describes the initial path of one of these particles immediately after entering region 1 

__ It curves toward the top of the page. 

__ It curves into the page. 

__ It moves in a straight line. 

Explain your reasoning. 

__ It curves toward the bottom of the page. 

__ It curves out of the page. 


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A constant magnetic field of magnitude B 2 directed into the page is now added in region 2 to the right of 

region 1, as represented in the figure below. Suppose a particle leaves the radioactive source, travels through 

region 1 in a straight line, and enters region 2. For each of the following, express algebraic answers in terms 

of E, B 1 , B2, q, and fundamental constants, as appropriate. 

B1 x x x x × 22× 

+++++++++++++ 

Region I Region 2 

(b) Determine an expression for the initial magnetic force on the particle in region 2 and state its direction. 

(c) Describe the changes, if any, in the magnitude and direction of the magnetic force as the particle moves 

in region 2. 

(d) Describe the path of the particle in region 2. 

(e) Derive an expression for the charge-to-mass ratio q/m of the particle. Specifically note any quantities not 

previously defined that are included in your answer. 


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Magnetic Field and Flux AP Problem

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