Physics Week 6(Sem. 2) Name____________________________ Chapter Summary Where μ0 is the permeability of free space, and its value is 4π x 10‐7 T m/A. I is current in Amps and r is radius in meters. This equation demonstrates why the magnetic field strength gets stronger as you approach the current carrying wire, where r is smaller. Magnetism Cont’d Motional EMF The current in a coil is called induced current, because it is brought about by a changing magnetic field. And since a source of emf is always needed to produce a current, the coil itself behaves as if it were a source of emf. This emf is called induced emf. Consider a rod of length (L) moving with a constant velocity of (v) perpendicular to a magnetic field (B). Due to RHR‐1, the electrons move creating a positive top side and a negative bottom. This separation of charges at the ends of the moving conductor gives rise to an induced emf called a motional emf. The fact that the electrical and magnetic forces balance at equilibrium can be used to determine the magnitude of the motional emf (ε). Therefore after some equation solving the motional emf (ε) is Magnetic Field of a Current Loop The right hand rule can also be applied to find the direction of the magnetic field of a current carrying loop. Regardless of where on the loop you apply the right hand rule, the field within the loop points in the same direction, upward. The field lines resemble those of a bar magnet. Solenoids produce a strong magnetic field by combining several loops. The magnetic field in a solenoid increases with current and the number of coils per unit length. When an iron rod is placed inside of the loops, it can be called an electromagnet (see fig. 21‐8). Magnetic Force on a Current carrying Wire Just like a charge experiences a magnetic force when it moves through a magnetic field, a current carrying wire also experiences a force when it is placed in a magnetic field. If a straight length of wire of length ( ), carrying a current (I) was in a magnetic field (B), the force it would experience would be: Where ε is in units of volts, v is a velocity in m/s, B is the magnetic field in Tesla (T), and L is the length of the rod in meters. As expected ε=0 when the =0, for no motional emf is developed in a stationary situation. Magnetic Field of a Current carrying wire As a charge moves in an electric field it experiences a magnetic force. Therefore charges moving through a current carrying wire create a magnetic field. The right hand rule #2 can be applied to determine the magnetic field around a wire. If your thumb is placed in the direction of the current then your right hand wraps in the direction of the magnetic field (B). To determine the magnitude of the magnetic field on a long straight current carrying wire the equation below can be applied 2
Ms. N. May Where Fmag would be the force the current carrying wire experienced. This equation is only valid when the current and the magnetic field are at right angles to each other. When applying the right hand rule your thumb will be placed in the direction of the current. If the magnetic field is into the page, then the direction of the magnetic force is to the left (see fig). Two parallel conducting wires Two parallel conducting wires exert forces on one another, since a current in a conductor creates its own magnetic field. When the current is in the same direction, the two wires attract to one another. This can be confirmed by the right hand rule. If the current in the two wires are going in opposite directions, the two wires will repel each other (see fig). Induced Current Suppose a bar magnet is pushed into a coil of wire. As the magnet moves into the coil, the strength of the magnetic field within the coils increases, and a current is induced in the circuit. This induced current in turn produces its own magnetic field, whose direction could be found using the right hand rule. As the magnet approaches, the magnetic filed lines passing through the coil increase in strength. The induced current in the coil must be in a direction that produces a magnetic field that opposes the increasing strength of the approaching field. The induced magnetic field is therefore in the direction opposite that of the approaching magnetic field (see fig 22‐4 &5). In figure 22‐4 the coil and the magnet repel one another and in figure 22‐5 they attract one another. Magnetic Flux Magnetic flux is analogous to electric flux, which deals with the electric field and the surface through which it passes. Therefore magnetic flux depends on the magnetic field and the surface through which it passes. Using the equation for motional emf (provided before) it can be rearranged to solve for magnetic flux. After some algebra the motional emf equation appears as Where BA is the area swept out by the rod moving a distance of x and having a length (l). When the magnetic flux is defined as BA it then takes on the symbol φ. Thus the motional emf equation is Ф
Ms. N. May Ф
Ф
In other words the induced emf equals the time rate of change of the magnetic flux. Often this equation is written as Ф/ , with the minus sign in it. Assigning the minus is important for universal application of the equation for the following reason. The direction of the current induced in the circuit is such that the magnetic force (F) acts on the rod to oppose its motion, thereby tending to slow down the rod. A general equation for magnetic flux such that the component of the magnetic field is perpendicular to the surface must be used. Thus the magnetic flux equation is Ф
ө
Where Ф is magnetic flux in units of T m2 or Weber (Wb). Len’z Law The rule for finding the direction of the induces current is called Lenz’s law and says “ the magnetic field of the induced current opposes the change in the applied magnetic field.” Note that the field of the induced current does not oppose the applied field but rather the change in the applied field. If the applied field changes, the induced field attempts to keep the total field strength constant, according to the principle of energy conservation. Faraday’s law of induction Due to the principle of energy conservation, Lenz’s law allows you to determine the direction of an induced current in a circuit. Lenz’s law does not provide information on the magnitude of the induced current or the induced emf(electromotive force). To calculate the magnitude of the induced emf, you must use Faraday’s law of magnetic induction. For a single loop of a circuit, the equation may be Ф
∆
Where N is the number of coils, Ф is the change in magnetic flux for 1 loop, and is the time interval during which the magnetic flux changed. Ms. N. May Ms. N. May Ms. N. May Ms. N. May Ms. N. May Ms. N. May Ms. N. May 1. Two long parallel wires, fixed a distance d
apart in space, each carry a current I.
The force of attraction between them is F.
Which other arrangement of currents in
long parallel wires would produce the
same force F?
(1) a current of 3I and a distance of 6d
(2) a current of 6I and a distance of 3d
(3) a current of 3I and a distance of 3d
(4) a current of 9I and a distance of 3d
(5) a current of 3I and a distance of 9d
2. Two particles, with equal charge and
equal masses and velocities v1 and v2
travel in circular paths in a magnetic field
with radii R1 and R2 respectively. Which
of the following must be true?
(1) The velocities must be equal but the
radii might not be.
(2) R1v1 = R2v2
(3) R1v2 = R2v1
(4) The radii must be equal but the
velocities might not be.
(5) Both the radii and the velocities must
be equal.
3. If two current carrying wires exert a force
of 50 N on each other, what force will they
feel if the distance between them is
halved?
(1) 12.5 N
(4) 25 N
(2) 50 N
(5) 200 N
(3) 100 N
4. Two long, straight, parallel wires 0.24 m
apart are carrying the same current I in
the same direction. The force per unit
length felt by one wire from the other is 2
N/m. Find the value of the current I.
(4) 2.34 × 10–4 A
(1) 1.55 × 103 A
(5) 1.55 × 10–4 A
(2) 4.55 × 103 A
(3) 2.34 × 103 A
6. Two long, straight, parallel wires are
placed a distance d apart. A current of I
runs through each, in opposite directions.
The force per unit length on each wire is
(1) attractive, magnitude (µ0/2p)I/d
(2) attractive, magnitude (µ0/2p)I2/d2
(3) repulsive, magnitude (µ0/2p)I2/d
(4) repulsive, magnitude (µ0/2p)I/d
(5) repulsive, magnitude (µ0/2p)I2/d
7. Two long, straight, parallel wires are a
distance d apart. Wire A carries a current
of I, Wire B carries a current 2I. The ratio
of the force on Wire A to the force on Wire
B is
(1) 1:4
(4) 4:1
(2) 1:1
(5) 1:2
(3) 2:1
8. A wire in the plane of the page carries a
current I directed toward the bottom of
the page. If the wire is located in a
uniform magnetic field B directed out of
the page, the force on the wire resulting
from the magnetic field is
(1) directed to the right
(2) directed into the page
(3) directed to the left
(4) directed out of the page
(5) zero
9. A wire in the plane of the page carries a
current I directed toward the bottom of
the page. If the wire is located in a
uniform magnetic field B directed toward
the top of the page, the force on the wire
resulting from the magnetic field is
(1) zero
(2) directed into the page
(3) directed to the left
(4) directed to the right
(5) directed out of the page
5. If two current carrying wires exert a force 10. The units J/A can be used to express
(1) resistance
of 10 N on each other, what force will they
feel if the distance between them is
(2) electric field strength
doubled?
(3) magnetic field strength
(1) 20 N
(4) 5 N
(4) magnetic flux
(5) capacitance
(2) 10 N
(5) 2.5 N
(3) 40 N
11. Base your answer to the following
question on the diagram below.
In the picture above, a segment of
length l of a current carrying wire is
suspended by a string in a uniform
magnetic field going out of the page. What is the tension T on the string?
(1) mg + IBl
(4) mg – IBl
(2) mg – IB/2
(5) (BI – l/2) + mg
(3) g + lB
12.
13. The force acting on long current carrying
wire in a magnetic field is affected by all
of the following EXCEPT
(1) the length of strength of the magnetic
field.
(2) angle between the wire and the
direction of the magnetic field.
(3) the voltage across the wire.
(4) the current in the wire.
(5) the direction of current flow.
14. Two long parallel wires are fixed at a
distance d apart and each carry a current
of I. The force of attraction between them
is F. If the distance between the wires is
doubled and the current in each of the
wires is doubled, what is the new force of
attraction between the wires?
(1) 4F
(4) F/2
(2) 2F
(5) F/4
(3) F
15. Two long parallel wires carry unequal
currents in opposite directions. One of
the currents is much greater than the
other. Compared to the force felt by the
wire with the smaller current the force felt
by the wire with the greater current is
(1) smaller and in the same direction
(2) greater and in the same direction
(3) equal and in the same direction
(4) equal and in the opposite direction
(5) smaller and in the opposite direction
A long straight wire of length 20 m with a
mass per unit length of 0.25 kg/m is lying
across the ground perpendicular to a
16. The magnetic field due to a long straight
uniform magnetic field of 4.5 T out of the
wire at a distance d from it has a
page as shown in the picture above. How
magnitude B. If the current in the wire is
much, and in which direction, must
doubled, the magnetic field at a distance
current flow to reduce the normal force on
d would be.
the wire to 0 N?
(1) 2B
(1) 1.1 A from right to left
(2) B
(2) 0.11 A from left to right
(3) 12B
(3) 1.1 A from left to right
(4) 4B
(4) 0.11 A from right to left
(5) 14B
(5) 0.55 A from right to left
17. A long straight wire carries a current of 3
A. Find the magnitude of the magnetic
field 6 cm from the wire.
(4) 1 × 10–4 T
(1) 2 × 10–6 T
(2) 1 × 10–5 T
(5) 2 × 10–5 T
(3) 1 × 10–6 T
18. Two long straight intersecting wires carry
currents I in the directions shown.
Which direction is the magnetic field
pointed at the point P?
(1) into the page
(2) the magnetic field at point P is zero.
(3) towards the top of the page
(4) out of the page
(5) towards the bottom of the page
19.
20. Which of the following are true about
electromagnetic forces and fields?
I. The magnetic field lines due to a
current-carrying wire radiate away
from the
wire.
II. Electric field lines due to a currentcarrying
wire circle the wire and their direction
is
determined by the right hand rule.
III. Magnetic force vectors and electric
force
vectors for a charged particle always
point in
opposite directions.
(1) I and II only
(2) III only
(3) I and III only
(4) none of the above are true
(5) I, II, and III
21. If the resistance of a long straight wire is
doubled and the voltage remains
constant, the magnetic field produced by
the wire
(1) the magnetic field is not influenced by
a change in resistance
(2) decreases by a factor of 2
(3) increased by a factor of 2
(4) decreases by a factor of 4
(5) increase by a factor of 4
Two long, straight, parallel wires are
separated by a distance d, as shown
above. They each carry a steady current I 22. A charged particle is a certain distance
away from a current-carrying wire. The
into the page. At what points in the plane
particle is moving at a constant velocity,
of the page and outside the wires, besides
perpendicular to the magnetic field
the points at infinity is the magnetic field
produced by the wire. If the current
due to the currents zero.
traveling through the wire and the
(1) Only at point P
velocity of the particle are doubled, the
(2) At all points on the line connecting the
force on the particle two wires
(1) remains the same
(3) At all points on the line AA'
(2) increases by a factor of 4
(4) At no points
(3) increases by a factor of 2
(5) At all points on a circle of radius 2d
(4) decreases by a factor of 4
centered at point P
(5) increases by a factor of 8
23. What is the magnetic field due to a
circular loop of wire carrying a current I
and having a radius R at the center of the
loop?
(1) ƒ0I/4R
(2) ƒ0I/2R
(3) 2pƒ0IR
(4) ƒ0I/2pR
(5) ƒ0I/4pR
24. A tightly-wound solenoid has a length of
50 cm and contains a total of 200 turns.
If it carries a current of 3 A, what is the
magnetic field inside the solenoid?
(1) 1200ƒ0
(2) 600ƒ0
(3) 300ƒ0
(4) 2400ƒ0
(5) 100ƒ0
25. A square loop of wire with sides of 0.20 m
is oriented at an angle of 30º to a
constant magnetic field of strength 3.0 T.
The magnetic flux through this loop is
most nearly
(1) 6.4 Wb
(4) 0.12 Wb
(2) 0.06 Wb
(5) 75 Wb
(3) 0.10 Wb
26. A loop of wire forms a right triangle with
legs of length 3 m and 4 m. The loop is
placed in a magnetic field of 5 T at a 45°
to the magnetic field. What is the
magnetic flux through the loop?
(4) 30 T•m2
(1) 26 T•m2
(2) 21 T•m2
(5) 15 T•m2
(3) 42 T•m2
28.
A circular wire loop is at rest in a uniform
magnetic field of magnitude 10T that is
directed into the page. The loop has a
diameter of 6 cm, and the plane of the
loop is perpendicular to the field, as
shown above. The total magnetic flux
through the loop is
(4) 36p × 10–3 T•m
(1) 6p × 10–3 T•m
2
2
(2) 36p2 × 10–3 T•m (5) 0 T•m2
2
(3) 9p × 10–3 T•m
2
29. Which expression is a unit of potential
difference equivalent to a volt?
(1) Tesla × meter
second
(2) Tesla × meter
second2
(3) Tesla × second
meter2
(4) Tesla × meter2
second
(5) Tesla × second
meter
27. A straight rod of length 3.0 m is held
perpendicular to a magnetic field of 2.0 T.
It is rotated about its midpoint at a rate of 30. The magnetic field from a loop of current
carrying wire in the plane of the page is
5.0 revolutions per second, remaining
directed out of the page. In which
perpendicular to the field the entire time.
direction do the electrons in the wire loop
The emf generated in the rod is most
move?
nearly
(1) they all move to the left side of the loop
(1) 141 V
(4) 22.5 V
(2) counterclockwise
(2) 94.2 V
(5) 70.7 V
(3) clockwise
(3) 45 V
(4) they all move to the right side of the
loop
(5) they are stationary
31.
A conducting loop with a radius of 0.25 m
an internal resistance of 4.0Ω is situated
in a 12.0 T magnetic field directed into
the page as shown. If the area of the loop
is shrinking at a rate of 0.05 m2/s, what
is the induced current in the loop?
(1) 0.60 A counterclockwise
(2) 0.60 A clockwise
(3) 1.2 A clockwise
(4) 0.15 A counterclockwise
(5) 0.15 A clockwise
32. Base your answer to the following
question on the diagram below of two
square loops of the same wire, one with
side length a and side length 2a. A
uniform magnetic field B directed into the
page is contained within the area
enclosed by the square of side a.
33. A long straight wire has an internal
resistance of 2.5 Ω/m. If it moves at 4
m/s in a 5 T magnetic field, what is the
magnitude of the force per unit length
opposing its motion?
(1) 8 N/m
(4) 10 N/m
(2) 5 N/m
(5) 20 N/m
(3) 40 N/m
34. Lenz's law concerning induced emf can be
shown to directly follow from
(1) Conservation of Charge
(2) Conservation of Energy
(3) Newton's Second Law of Motion
(4) Gauss's Law
(5) Coulomb's Law
35. A bar magnet is dropped through a loop
of wire at a constant velocity. The net
amount of current that flowed through a
given point in the wire is I when the
magnet is exactly halfway through the
loop. What is the total amount of current
that will have flowed through the same
point when the magnet has passed
completely through the loop?
(1) –2I
(4) I
(2) –I
(5) 2I
(3) 0
36. Which of the following creates a magnetic
field?
The magnetic field B varies at a constant
rate such that the current induced in the
wire with side a is I. Find the current
induced in the loop with side 2a.
(1) 4I
(2) I2I
(3) 2I
(4) I4I
(5) I
I. Moving electric charges
II. Stationary electric charges
III. Time changing electric fields
(1) III only
(4) II and III only
(2) I and II only
(5) I, II, and III
(3) I and III only