For the wire carrying a flow of electrons in the direction shown, is the magnetic field at point P

-

P

(a) to the right

(b) to the left

(c) up

(d) into the screen

(e) out of the screen

B

R

P Q I

I

In the figure below, which is the direction of the magnetic field at point…

(c)(a) (d) (e)(b)

1) …P? 2) …Q? 3)…R?

In the figure above, where is the magnetic field the weakest?

(a) point P

(b) point Q

(c) point R

Ids

1

ds

2 ds

3

ds

4

r1

r2

r3

r4

The magnetic field at P due to the current I in

Biot - Savart law

dB k Ids r

rm

2

Is directed

(a) into the screen (b) out of the screen

(c) up (d) down

(e) zero

11. ds

22. ds

33. ds

44. ds

P

I

ds

r

Biot - Savart law: dB k Ids r

rm

2

PI

The magnitude of the magnetic field contribution from the current element above isds

2

2

2

1 sin 90)

cos90)

1 sin)

) none of the above

o

m

o

m

m

dsa dB k I

r

ds rb dB k I

rds

c dB k Ir

d

I

ds

Biot - Savart law:2

2

ˆ

sin 90

m

o

m

ds rB dB k I

r

IdsdB k

r

PIThe total magnetic field at P

from the current in the wire shown on the right is:

a B kI r

r

b B kI r

r

c B kI r

r

d B kI ds

re

P m

P m

P m

P m

o

)

)

)

)sin

)

no ne o f the ab o ve

2

2

2

2

2

2

9 0

I13

P

nr1r2

r3

2

so

dB k Ids r

r

dB dB k Ids r

r

m

m

sin

2

2

The Biot-Savart law for the contribution to the magnetic field from a current element is given on the right.I ds

I) Is the ‘r’ given by (a) r1 (b) r2 (c) r3 ?

II) Is the given by (a) 1 (b) 2 (c) 3 ?

III) Is the direction of at P

(a) up (b) down

(c)into page (d)out of page

Use the figure to answer the following questions about the Biot-Savart Law

Ids

r

r

r = r vec to r o f length 1 in the d irec tio n

Magnetic field from a section of a straight wire

2Biot Savart law: m

ds rdB k I

r

2 2

2 2

1 sin( ) ( )

cos r sin( ) ( )

( ) None of the above

m m

m m

ds I dsa dB k I b dB k

r rI ds I ds

c dB k d dB kr r

e

The magnitude of the magnetic field at P due to the current I in is

ds

Magnetic field from a section of a straight wire

P

a

I

12

Bk I

aPm co s co s 1 2

Given the equation and figure on the right, what is the field at P due to an infinitely long wire carrying current I?

ak I

a

bk I

a

ck I

a

dk I

ae

m o o

m o o

m o o

m o o

) co s co s

) co s co s

) co s co s

) co s co s

)

B

B

B

B

no ne o f the ab o ve

P

P

P

P

4 0 1 5 0

0 3 6 0

0 1 8 0

1 8 0 0

The magnetic field at a distance “a” from a straight wire carrying current I is given in Figure 1. Therefore, the field at point P in Figure 2 is:

(a) 3 cos30 cos150

(b) 0

(c) 3 cos 60 cos0

(d) 2

o omP

P

o omP

mP

k IB

aB

k IB

ak I

Ba

P

aI

12

Bk I

aPm co s co s 1 2

P

a

a aI I

I

Equilateraltriangle

Figure 1 Figure 2

P

I

I

For the two long wires on the right, the vector magnetic field at P is best represented by where...

B p

B P

(a)

B P

P

P

(d)

B P

P

(b)

B P

P(c)

(e) none of the above

Two wires carry equal currents I1 into the screen, each producing a magnetic field B1 at point P

I1

I1

x

yP

The total field at P is given by

1 1

1 1

1

(a) (b) 2

ˆ ˆ(c) 2 cos (d) -2 cos

ˆ(e) -2 sin

B B

B x B y

B y

I Px

dsu

dsd

Perspectiveview

Top viewdB I

ds r

ro

4 2

dsu

dsd

Px

dB1dB 2

dB 3

dB 4 dB5

dB 6

Magnetic field on the axis of a circular turn of wire

1. Which best represents the field at P from i) and ii) ? I dsu

dI ds

dB1(a) 2dB(b) 3dB(c) 4dB(d) 5dB(e)

2. Which best represents the total field at P?

dB1(a) 2dB(b) 3dB(c) 4dB(d) 6dB(e)

Which of the following is the equation for the magnetic field on the axis of a solenoid?

a BIR

x R

b BN I

c BI

ad

o

o

o

)( )

) co s co s

) co s co s

)

no ne o f the ab o ve

2

2 2

1 2

1 2

2

2

4

Magnetic field on the axis of a solenoid

Magnetic field on the axis of a solenoid

LI

I

N

L tu rn s p er m ete r

P2 P1

12

BN I

LPo

2 1 2co s co s

1. Is the field at P1 directed

(a) to the right

(b) to the left

(c) neither

(a) (b) (c) 2 (d) none of these2

oo o

NI NI NI

L L L

2. Near the centre of a long solenoid, is

3. Near one end of a long solenoid, is

(a) (b) (c) 2 (d) none of these2

oo o

NI NI NI

L L L

B P2

1PB

Three equations from the formula sheet are given below for the magnetic field caused by a current I.

BIR

R xPo

2

2 2 3 22 ( ) /

BN I

LPo

2 1 2[co s co s ]

Bk I

aI

a

pm

o

(co s co s )

(co s co s )

1 2

1 24

Which of these is the correct one to use for the magnetic field…

1. …at a given distance from a straight wire

2. …on the axis of a circular turn

3. …on the axis of a solenoid (coil)

(c)

(a) (b)

Assuming B= 0 just outside the coil, use Ampere's law and the dotted path provided to determine the field B on the axis of the coil.

w

L

w

I

I

N

mN

L

tu rn s

(a) (b)

(c) (d) None of the above

oo

o

IB B I m

LI m

BL

Current I flows in the coil on the right

B ds Io enclosed Ampere's law:

L

I

I

N

mN

L

tu rn s

Current I flows in the coil on the right

B ds Io enclosed Ampere's law:

(b) Sketch the shape and direction of the magnetic field near a turn adjacent to the one in (a).

(c) Do the fields in (a) and (b) add or subtract along the axis of the coil?

(d) Do these fields in (a) and (b) add or subtract in the region between two adjacent wires?

(e) Draw a magnetic field line just inside the line of wires on the bottom of the coil.

Redraw the coil on your page, and (a) Sketch the shape and direction of the magnetic field near one of the wire turns at the bottom.

L

I

I

N

mN

L

tu rn s

Current I flows in the coil on the right

B ds Io enclosed Ampere's law:

(2) Does the field in (a) reinforce or cancel the corresponding field from a turn at the bottom of the coil?

Inside the coil: (a) reinforce (b) cancel

Outside the coil: (a) reinforce (b) cancel

(3) From our discussion to date, sketch a few field lines around and inside the whole coil. Remember that the field lines are closest together where B is strongest.

Redraw the coil on your page, and

(1) Sketch the shape and direction of the magnetic field near one of the wire turns at the top.

Ampere's law:

The magnetic field lines around a solenoid look roughly as sketched on the right

B ds Io enclosed

I

I

B

I (into screen)

I (out of screen)To calculate B on the axis of the solenoid, select a closed path, containing some current and consisting of several segments, such that for each segment either (i) B ~ 0, or (ii) path, or (iii) B ~ constant and path

.

B B

I

I(a) (b) (c)

Either (b) or (c)

(d)

rR

Pds

B ds Io enclosed Ampere's law:

A large wire of radius R carries a current I0 into the screen as sketched on the right. The current is uniformly distributed over the wire. Ampère's law is used to determine the magnetic field strength B at a distance r from the centre of the wire.

1. For the dashed path, how much current is Ienclosed?

(a) I0 (b) (c) (d)

r

RI 0

R

rI 0

r

RI

2

2 0

2. At point P, is : (a) B ds (b) zero (c) can't tell?

3. Which is the correct result for B(r) from Ampère's law?

B r ds I enclosed( ) 0B r r I enclosed( ) 20

B r r I enclosed( ) 0

B r r I enclosed( ) 4 20 B r r I enclosed( ) 2 0

B ds

(a)

(b)

(c)

(d)

(e)

- v

B into screen

What is the direction of the force on the particle?

(a) into screen (b) out of screen (c) up

(d) down (e) to right

Does the particle rotate

(a) clockwise? (b) counterclockwise?

F qv B

For a charged particle moving with velocity in a circle in a magnetic field , which of the following is most correct?

(a) (b) (c)

(d) (e) a, b and c

BvqF

r

mvF

2

sinqvBF

r

vmF

2

Which of the following is the correct angular velocityof a particle of charge q moving perpendicular to a magnetic field B?

(a) (b) (c)

(d) (e) m

qB

m

B qvBm

qB

m

m

qvB

v

B

I Iq

v

What is the direction of the magnetic force on the negative particle q below, caused by the magnetic field from the wire?

a) Up

b) Down

c) Into screen

d) Out of screen

F qv B

(From pre-class quiz)Distribution of charge in a current sheet, in a magnetic fieldA steady conventional current, I, is flowing northward in a horizontal conducting sheet, and a magnetic field is oriented downwards through the sheet. Which of the following statements is true?

a. The East edge of the sheet will carry no net charge.b. The East edge of the sheet is positively charged.c. The East edge of the sheet is negatively charged.d. Both the East and the West edges of the sheet are positively charged. 

yx

z

c ab

d

I

I

B

1. Which side of the metal ribbon shown on the right is positive?

(a) a (b) b

(c) c (d) d

2. What direction is the electric field in the ribbon, caused by the magnetic field?

ˆ ˆ ˆ(a) (b) (c)

ˆ ˆ(d) (e)

x x y

y z

II

B into the p age

wire

F I Bo n w ire

The charge carriers in the wire are electrons. What is the direction of the magnetic force on the wire?

(a) out of the page (b) up

(c) down (d) to right

(e) to left

B

A

F I B Two long wires carry current into the screen.

1. What is the direction of the magnetic field at B caused by A?

(a) to the right (b) to the left (c) up (d) down

2. Is the direction of the force on B

(a) up (b) down (c) into screen

(d) out of screen (e) to the left

3. Do the two wires

(a) attract each other (b) repel each other

(c) neither

Two long parallel wires carry currents, I1 into the screen and I2 > I1 out of the screen.1. What is the direction of the force on i) wire #1? ii) wire #2?

#1 #2I2 > I1I1

2. Compared to the force on wire #1, the force on #2 is

(a) greater (b) smaller (c) the same?

(a) (b) (c) (d) (e)No force

3. What entirely independent method could you use to determine the direction in question 1. ii) given the answer in 1. i)?

A rectangular loop is placed in a uniformmagnetic field with the plane of the loopperpendicular to the direction of the field.If a current is made to flow through the loopin the sense shown by the arrows, the fieldexerts on the loop:

1. a net force.2. a net torque.3. a net force and a net torque.4. neither a net force nor a net torque.PI

I

B

A rectangular loop is placed in a uniformmagnetic field with the plane of the loopparallel to the direction of the field.If a current is made to flow through the loopin the sense shown by the arrows, the fieldexerts on the loop:

1. a net force.2. a net torque.3. a net force and a net torque.4. neither a net force nor a net torque.PI

I

B

What is for this current loop?A

xz

y 2

1

IA B

1 2 1 2

ˆ ˆ) )

ˆ ˆ) )

a Iz b Iz

c z d z

N S

l1

I

B

B

l2

Top view

xy

z

l2

A rectangular loop of wire carries a current I in a magnetic field

B

Which of the following gives the force on one side of the loop?

1 2

1 1

2

(a) (b)

(c) cos (d) sin

(e) sin

F Il B F Il B

F Il B F Il B

F Il B

F I B

N S

Top view

xy

z

A rectangular loop of wire carries a current I in a magnetic field

B

In which direction does the coil rotate (direction of angular velocity )?

ˆ ˆ ˆ(a) (b) (c)

ˆ ˆ(d) (e)

x y y

z z

B

N S

N S

l1

I

B

B

l2

Top view

xy

z

l2

A rectangular loop of wire carries a current I in a magnetic field

B

Which of the following gives the torque on the loop?

1 1 2

1 2 1 2

1 2

(a) cos (b) cos

(c) sin (d) 2 sin

(e)

Il B Il l B

Il l B Il l B

Il l B

IA B

P

If the current flows through the galvanometer coil in the direction of the bold arrows, does the pointer P deflect ?

(a) clockwise

(b) counterclockwise

(c) not enough information to tell

The Galvanometer