1. Three long, parallel conductors each carry a current of ...

1. Three long, parallel conductors each carry a current of I. The figure below is an end view of the conductors, with each current coming out of the page. Dtermine the magnitude and direction of the magnetic field at the following points.

#1 (a) point A

2a

B2 B 45o 45o 1 B3

#3 x

#2

y

Directions of B1 (magnetic field due to current #1), B2, and B3 are determined by right hand

rule, indicated in the figure above.

x - components :

|

B1

||

B2

|

0I 2a 2

B1x

|

B1

| sin

45 o

|

B1

|

1 0I 2 2a 2

1 0I 2 4a

B 2x

-

|

B2

| sin

45 o

|

B2

|

1 0I 2 2a 2

1 0I 2 4a

B3x 0

B x

B 1x

B2x

B3x

0I 4a

0I 4a

00

y - components :

B1y

|

B1

| cos

45 o

|

B1

|

1 0I 2 2a 2

1 2

0I 4a

B 2y

|

B2

| cos

45 o

|

B2

|

1 0I 2 2a 2

1 0I 2 4a

B 3y

|

B2

|

0I 2 (3a)

0I 6a

B y

B 1y

B2y

B3y

0I 4a

0I 4a

0I 6a

20I 3a

Magnitude 20I 3a

Direction : Downward

(b) point B

#1

2a

B2

B1

B3

#3 x

#2

y

Directions of B1 (magnetic field due to current #1), B2, and B3 are determined by right hand rule, indicated in the figure above

x - components :

|

B1

||

B2

|

0I 2a 2

B1x

|

B1

|

0I 2a 2

B 2x

-

|

B2

|

0I 2a 2

B3x 0

B x

B 1x

B2x

B3x

0I 2a 2

0I 2a 2

00

y - components :

B1y 0

B2y 0

B 3y

|

B3

|

0I 2 (2a)

0I 4a

B x

B 1x

B2x

B3x

00

0I 4a

0I 4a

Magnitude 0I 4a

Direction : Downward

(c) point C

#1 2a

B2

B1

#3

45o 45o

B3

x

#2

y

Directions of B1 (magnetic field due to current #1), B2, and B3 are determined by right hand rule, indicated in the figure above

x - components :

|

B1

||

B2

|

0I 2a 2

B1x

|

B1

| cos

45 o

|

B1

|

1 0I 2 2a 2

1 2

0I 4a

B 2x

-

|

B2

| cos

45 o

|

B2

|

1 0I 2 2a 2

1 2

0I 4a

B3x 0

Bx

B 1x

B2x

B3x

0I 4a

0I 4a

00

y - components :

B1y

-

|

B1

| sin45o

|

B1

|

1 0I 2 2a 2

1 2

0I 4a

B 2y

-

|

B2

| sin

45 o

|

B2

|

1 0I 2 2a 2

1 2

0I 4a

B 3y

|

B2

|

0I 2a

B y

B 1y

B2y

B3y

0I 4a

0I 4a

0I 2a

0

Magnitude 0

Direction : No direction

2. Two long, parallel wires carry currents of I1 and I2 in the directions indicated in the figure below. Take the positive x direction to be to the right.

(a) Find the magnitude and direction of the magnetic field at a point midway between the wires.

B1

y

x

B2

Directions of B1 (magnetic field due to current #1)and B2 are determined by right hand rule, indicated in the figure above

x - components :

B1x 0

B2x 0

Bx B1x B2x 0

y - components :

|

B1

|

0 I1 2 d

0 I1 d

2

and

|

B2

|

0I2 2 d

0I2 d

2

B1y

|

B1

|

0 I1 d

B 2y

-

|

B2

|

0I 2 d

B y

B 1y

B2y

0 I1 d

0I2 d

0 d

(I1 - I2 )

Magnitude

0 d

|

I1

-

I2

|

Direction : Upward if I1 I2 , downward if I1 I2

(b) Find the magnitude and wire carrying current I2.

direction

of

theB1magnetic

field

at

point

P,

located

d

above

the

B2

45o

y

2d

x

Directions of B1 (magnetic field due to current #1)and B2 are determined by right hand rule, indicated in the figure above

|

B1

|

0 I1 2d 2

and

|

B2

|

0I2 2d

x - components :

B1x

|

B1

|

0 I1 2d 2

cos

45 o

0I1 2d 2

1 2

0I1 4d

B 2x

|

B2

|

0I 2 2d

B x

B 1x

B2x

0 I1 4d

0I2 2d

0 4d

(I1

2I2 )

B B1 B2

y - components :

B1y

|

B1

| sin

45 o

0 I1 2d 2

1 0I1 2 4d

B2y 0

B y

B 1y

B2y

0 I1 4d

0

0 I1 4d

Magnitude

[

0 4d

(I1

2I2 )]2

[

0 4d

I1

]2

0I 4d

(I1 2I2 )2 I12

0I 4d

2I12 4I1I2 4I22

180o

tan

-1

| |

By By

| |

0 I1

180 o

tan -1

0 4d

4d (I1

2I2 )

180 o

tan -1

I1

I 1 2I2

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