week 8users.physics.ucsd.edu/2009/spring/physics2ba/08.pdf · 2009. 3. 15. · using the right-hand...

week 8The Magnetic Field

General Principles

Applications

Start with magneticforces on moving charges and

currents

1) out of the page

2) into the page

3) downwards

4) to the right

5) to the left

A positive charge enters a

uniform magnetic field as shown. What is the direction of the magnetic force?

x x x x x x

x x x x x x

x x x x x x

v

q

Using the right-hand rule, you can

see that the magnetic force is

directed to the left. Remember

that the magnetic force must be

perpendicular to BOTH the B field

and the velocity.

1) out of the page

2) into the page

3) downwards

4) to the right

5) to the left



x x x x x x

x x x x x x

x x x x x x

v

qF

1) out of the page

2) into the page

3) downwards

4) upwards

5) to the left

x x x x x x

x x x x x x

x x x x x xvq





directed upwards. Remember



and the velocity.

1) out of the page

2) into the page

3) downwards

4) upwards

5) to the left

x x x x x x

x x x x x x

x x x x x xvq

F



1) out of the page

2) into the page

3) zero

4) to the right

5) to the left

® ® ® ® ®

® ® ® ® ®® ® ® ® ®

® ® ® ® ®

v

q


uniform magnetic field as shown. What is the direction of the magnetic force? (here “R” stands for pointing to the Right)



directed into the page. Remember



and the velocity.

1) out of the page

2) into the page

3) zero

4) to the right

5) to the left

® ® ® ® ®

® ® ® ® ®® ® ® ® ®

® ® ® ® ®

v

qF×



↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑

↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑

↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑

↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑

v

q

1) out of the page

2) into the page

3) zero

4) to the right

5) to the left



The charge is moving parallel to

the magnetic field, so it does not

experience any magnetic force.

Remember that the magnetic force

is given by: F = v B sin(θ) .

↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑

↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑

↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑

↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑

v

q

F = 0

1) out of the page

2) into the page

3) zero

4) to the right

5) to the left



An electron moves in the magnetic field of magnitude 0.50 T with a speed of1.0 x 107 m/s in the direction shown in the figure.What is the magnetic force on the electron?

Ans: 8.0 x 10-13 N, in direction of negative z-axis

x x x x x x x x x x x x






1

2

34

A beam of atoms enters

a magnetic field region.

What path will the

atoms follow?

Atoms are neutral objects whose net charge is zero.

Thus they do not experience a magnetic force.







1

2

34

A beam of atoms enters

a magnetic field region.

What path will the

atoms follow?

Follow-up: What charge would follow path #3? What about path #1?

x

y

A proton beam enters into a magnetic field region as shown below. What is the direction of the magnetic field B?

1) + y

2) – y

3) + x

4) + z (out of page)

5) – z (into page)

The picture shows the force acting

in the +y direction. Applying the

right-hand rule leads to a B field

that points into the page. The B

field must be out of the plane

because B ⊥ v and B ⊥ F.

x

y

A proton beam enters into a magnetic field region as shown below. What is the direction of the magnetic field B?

1) + y

2) – y

3) + x


5) – z (into page)

Follow-up: What would happen to a beam of atoms?

The Hall voltage across a 1.0-mm-thick conductor in a 1.0 T magnetic field is3.2 μV when the current is 15 A. What is the charge-carrier density in this conductor?

Ans: 2.9 x 1028 m-3 (Derive V=IB/e n t first)







1 2

Two particles of the same mass

enter a magnetic field with the same speed and follow the paths shown. Which particle has the bigger charge?

3) both charges are equal

4) impossible to tell from the picture

The relevant equation for us is:

According to this equation, the

bigger the charge, the smaller the radius.







1 2

Two particles of the same mass

enter a magnetic field with the same speed and follow the paths shown. Which particle has the bigger charge?

3) both charges are equal

4) impossible to tell from the picture

Follow-up: What is the sign of the charges in the picture?

1) it increases

2) it decreases

3) it stays the same

4) depends on the velocity direction

5) depends on the B field direction

A proton enters a uniform

magnetic field that is perpendicular to the proton’s velocity. What happens to the kinetic energy of the proton?






The velocity of the proton

changes direction but the

magnitude (speed) doesn’t

change. Thus the kinetic

energy stays the same.

1) it increases

2) it decreases

3) it stays the same

4) depends on the velocity direction

5) depends on the B field direction

A proton enters a uniform

magnetic field that is perpendicular to the proton’s velocity. What happens to the kinetic energy of the proton?






What direction would a B field

have to point for a beam of electrons moving to the right to go undeflected through a region where there is a uniform electric field pointing vertically upward?

1) up (parallel to E )

2) down (antiparallel to E )

3) into the page

4) out of the page

5) impossible to accomplish

electrons

E

v

B = ?

Without a B field, the electrons feel an electric force downwards. In order to compensate, the magnetic force has to point upwards. Using the right-hand rule and the fact that the electrons are negatively charged leads to a B field pointing out of the page.

What direction would a B field

have to point for a beam of electrons moving to the right to go undeflected through a region where there is a uniform electric field pointing vertically upward?

1) up (parallel to E )

2) down (antiparallel to E )

3) into the page

4) out of the page

5) impossible to accomplish

electrons

E

v

B = ?

A horizontal wire carries a current

and is in a vertical magnetic field.

What is the direction of the force

on the wire?

1) left

2) right

3) zero

4) into the page

5) out of the page

B

I

Using the right-hand rule, we see that the magnetic force must point out of the page. Since F must be perpendicular to both I and B, you should realize that F cannot be in the plane of the page at all.



What is the direction of the force on

the wire?

1) left

2) right

3) zero

4) into the page

5) out of the page

B

I

B

I

1) left

2) right

3) zero

4) into the page

5) out of the page



What is the direction of the force

on the wire?

When the current is parallel to

the magnetic field lines, the force

on the wire is zero.

B

I

1) left

2) right

3) zero

4) into the page

5) out of the page



What is the direction of the force on

the wire?

B

x

z

y

A rectangular current loop is in

a uniform magnetic field. What

is the direction of the net force

on the loop?

1) + x

2) + y

3) zero

4) - x

5) - y

Using the right-hand rule, we find that

each of the four wire segments will

experience a force outwards from the

center of the loop. Thus, the forces of

the opposing segments cancel, so the net

force is zero.

A rectangular current loop is in

a uniform magnetic field. What

is the direction of the net force

on the loop?

1) + x

2) + y

3) zero

4) - x

5) - y

B

x

z

y

If there is a current in

the loop in the direction

shown, the loop will:

1) move up

2) move down

3) rotate clockwise

4) rotate counterclockwise

5) both rotate and move

N S

NS

B field out of NorthB field into South

Look at the North Pole: here the

magnetic field points to the right and

the current points out of the page.

The right-hand rule says that the force

must point up. At the south pole, the

same logic leads to a downward force.

Thus the loop rotates clockwise.

N S

F

F

1) move up

2) move down

3) rotate clockwise

4) rotate counterclockwise

5) both rotate and move

If there is a current in

the loop in the direction

shown, the loop will:

A circular loop of wire carries a constant current. If the loop is placed in a region of uniform magnetic field, the

net magnetic force on the loop is

A. perpendicular to the plane of the loop, in a direction given by a right-hand rule

B. perpendicular to the plane of the loop, in a direction given by a left-hand rule

C. in the same plane as the loop

D. zero

E. answer depends on the magnitude and direction of the current and on the magnitude and direction of the magnetic field

A circular loop of wire carries a constant current. If the loop is placed in a region of uniform magnetic

field, the net magnetic torque

on the loop

A. tends to orient the loop so that its plane is perpendicular to the direction of the magnetic field

B. tends to orient the loop so that its plane is edge-on to the direction of the magnetic field

C. tends to make the loop rotate around its axis

D. is zero

E. answer depends on the magnitude and direction of the current and on the magnitude and direction of the magnetic field

A square current loop 5.0 cm on each side carries a 500 mA current. The loop is in a 1.2 T uniform magnetic fields. The axis of the loop, perpendicular to the plane of the loop, is 30o away from the field direction. What is the magnitude of the torque on the current loop?

Ans: 7.5 × 10-4 N.m

Magnetic fielddue to a moving charge

or current

General Principles

Applications

P1

2

3

4

If the currents in these wires

have the same magnitude, but

opposite directions, what is the

direction of the magnetic field at

point P?

1) direction 1

2) direction 2

3) direction 3

4) direction 4

5) the B field is zero

Using the right-hand rule, we

can sketch the B fields due

to the two currents. Adding

them up as vectors gives a

total magnetic field pointing

downward.

P

1

2

3

4

If the currents in these wires

have the same magnitude, but

opposite directions, what is the

direction of the magnetic field at

point P?

1) direction 1

2) direction 2

3) direction 3

4) direction 4

5) the B field is zero

Each of the wires in the figures below carry the same current, either into or out of the page. In which case is the magnetic field at the center of the square greatest?

1) arrangement 1

2) arrangement 2

3) arrangement 3

4) same for all

1 2 3B=? B=?B=?

1 2 3

Each of the wires in the figures below carry the same current, either into or out of the page. In which case is the magnetic field at the center of the square greatest?

1) arrangement 1

2) arrangement 2

3) arrangement 3

4) same for all

What are the magnetic field strength and direction at the dot in the figure?

Ans: 2.83 x 10-16 T

Two long, straight wires are oriented

perpendicular to the xy–plane. They

carry currents of magnitude I in

opposite directions a shown.

At point P, the magnetic field due to

these currents

A. is in the positive x–direction

B. is in the negative x–direction

C. is in the positive y–direction

D. is in the negative y–direction

E. none of the above

What are the magnetic field strength and direction at points “a” to “c”?

Ans: Ba = Bc = 6.7 x 10-5 T out of page Bb = 2.0 x 10-4 T into page

Combine both

Applications

z

y

x

I+q

A positive charge moves parallel

to a wire. If a current is suddenly

turned on, which direction will

the force act?


2) - z (into page)

3) + x

4) - x

5) - y

Using the right-hand rule to determine the magnetic field produced by the wire, we find that at the position of the charge +q (to the left of the wire) the B field points out of the page. Applying the right-hand rule again for the magnetic force on the charge, we find that +q experiences a force in the +x direction.

z

y

x

I+q

A positive charge moves parallel

to a wire. If a current is suddenly

turned on, which direction will

the force act?


2) - z (into page)

3) + x

4) - x

5) - y

Two positive point charges move side by side in the same direction with the same velocity.

The magnetic force that the upper point charge exerts on the lower one

A. is directed toward the upper point charge (that is, the force is attractive)

B. is directed away from the upper point charge (that is, the force is repulsive)

C. is in the direction of the velocity

D. is opposite to the direction of the velocity

E. none of the above

Two straight wires run parallel to each other, each carrying a current in the direction shown below. The two wires experience a force in which direction?

1) toward each other

2) away from each other

3) there is no force

The current in each wire produces a magnetic field that is felt by the current of the other wire. Using the right-hand rule, we find that each wire experiences a force toward the other wire (i.e., an attractive force) when the currents are parallel (as shown).

Two straight wires run parallel to each other, each carrying a current in the direction shown below. The two wires experience a force in which direction?

1) toward each other

2) away from each other

3) there is no force

Follow-up: What happens when one of the currents is turned off?

Two long parallel wires separated by a distance d carry currents I1 and I2 in the same direction.What is the magnetic force per unit length between the wires?

Ans: μ0 I1 I2 / 2 π d

Note: This is used to define the Ampère and then the Coulomb.

P

I

What is the direction of the

magnetic field at the center

(point P) of the square loop

of current?

1) left

2) right

3) zero

4) into the page

5) out of the page

Use the right-hand rule for each

wire segment to find that each

segment has its B field pointing

out of the page at point P. P

I

What is the direction of the

magnetic field at the center

(point P) of the square loop

of current?

1) left

2) right

3) zero

4) into the page

5) out of the page

The figure shows, in cross section, three conductors that carry currents perpendicular to the plane of the figure.

If the currents I1, I2, and I3 all

have the same magnitude, for which path(s) is the line integral of the magnetic field equal to zero?

A. path a only

B. paths a and c

C. paths b and d

D. paths a, b, c, and d

E. answer depends on whether the integral goes clockwise or counterclockwise around the path

An application of Ampere’s law: the toroid (you MUST have studied the solenoid)See problem 54 (ch 33)

B =µ0NI

2πr

week 8users.physics.ucsd.edu/2009/spring/physics2ba/08.pdf · 2009. 3. 15. · using the right-hand...

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