Comprehensive Formula sheet - PHYS 272 1 = k = 9 × 10⁹ 4 περ N. m² C² C² le 1.6 x 10-19 C €8.85 x 10-12 μο T. m² 1 x 10-7 N. m² 4 π C m/s 1. The electric field of a point charge q: 2. The electric force on a charge q: F = qE 3. The electric field at a location on the dipole axis: 4 5. 6. 1 2qsr Eaxis ¯ 4π €。 (r−³)² (r+³)² The electric field at a location perpendicular to the dipole axis: 1 q s E₁ = 4 ΠΕ0 · [r² + (²)²] ³/² 3/2 If r >> s, Eaxis 4 περ 1 2qs r3 1 qs If rs, E₁ 4π € г³ For a location on the perpendicular axis of a uniformly charged rod and at a distance r from the center of the rod, the electric field: 1 9 Erod = If r >> L, Erod 4 περ 2+ r () 1 q 4 π Є。 r² 1 2q/L If Lr, Erod 4 περ I The electric field along the axis of a uniformly charged ring, a distance r from the center of the ring: 1 Ering = qr 4πЄo (R2+2)3/2 1 q If r >> R, Ering 4περ μ 1 q 7. The electric potential due to a point charge q: V = 8. 9. The change in the electric potential for a uniform electric field: AV = -E. A The change in the electric potential for non-uniform electric field: AV = -SE. di 10. The change in electric potential energy: AU = q AV 11. The magnetic field of a moving point charge: B = Ho qvxr 4πT 2 12. The magnetic field due to a current-carrying straight wire: 1 If R >> r, Ering qr 4π €。 R³ Ho Bwire = IL Но 21 If L≫r (long wire) Bwire = 4π r√r² + (L/2)² 4π r 13. The magnetic field of a current-carrying coil (A = πR²): μο 2IAN Ho 2IAN B If r> R B coil 4π (r² + R2)3/2' coil 4 π r3 B center 14. The magnetic field inside a long solenoid: HONI B 15. The magnetic field of a bar magnet: Bmagnet 16. Ohms' Law: V = IR 17. Electric Power: P = IV 18. Magnetic force on a moving charge: =qx 19. Magnetic force on a current carrying wire due to a uniform magnetic field: F = ILXB 20. Electric flux for a uniform electric field: * = Ē.ĥ A 21. Electric flux for any electric field: = √ Ē.ñ dA 22. Gauss's Law: 6 E. ñ dA = Σinside Eo 23. Magnetic flux for a uniform magnetic field: += B.nz. 24. Magnetic flux for any magnetic field: += √ B.ñ dA 25. Ampere's Law: $ B. dỉ = HoΣlinside 26. Faraday's Law: emf = - A mag At 27. The frequency of the wave: f = 1/T 28. The angular frequency: v = 2nf 29. The speed of the wave: v = λf 30. Index of refraction: n = c/v 31. Law of refraction (Snell's Law): n₁sine₁ = n₂sine₂ = Ho 2πIN 4TT R ) A long straight wire suspended in the air carries a conventional current of 5.38 A in the +y direction as shown in Figure (the wire runs along the y axis). At a particular instant a proton at location (-0.0212, 0, 0) m has velocity (0,-2×105,0) m/s. (Consider the charge of the proton: qp = 1.6×10-19 C). y ν x + 1. The direction of the magnetic field due to the wire at the location of the proton: OInto the page Out of the page OUpward ODownward 2. What is the (vector) magnetic field due to the wire at the location of the proton? = о 5.075x10^-5 >[T] 3. What is the (vector) magnetic force on the proton due to the current in the wire? F= < -1.624x10^18 0 0 >[N] 4. Now, consider the proton is moving along -z axis with velocity (0, 0, -2×105) m/s, the magnetic force acting on the proton will be: = 0 0 [N]

College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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Electric and magnetic interactions

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Comprehensive Formula sheet - PHYS 272
1
= k = 9 × 10⁹
4 περ
N. m²
C²
C²
le 1.6 x 10-19 C
€8.85 x 10-12
μο
T. m²
1 x 10-7
N. m²
4 π
C m/s
1.
The electric field of a point charge q:
2.
The electric force on a charge q:
F = qE
3.
The electric field at a location on the dipole axis:
4
5.
6.
1
2qsr
Eaxis
¯ 4π €。 (r−³)² (r+³)²
The electric field at a location perpendicular to the dipole axis:
1
q s
E₁ =
4 ΠΕ0
· [r² + (²)²] ³/²
3/2
If r >> s,
Eaxis
4 περ
1 2qs
r3
1 qs
If rs,
E₁
4π € г³
For a location on the perpendicular axis of a uniformly charged rod and at a distance r from the center of the rod,
the electric field:
1
9
Erod =
If r >> L,
Erod
4 περ
2+
r
()
1
q
4 π Є。 r²
1
2q/L
If Lr, Erod
4 περ
I
The electric field along the axis of a uniformly charged ring, a distance r from the center of the ring:
1
Ering =
qr
4πЄo (R2+2)3/2
1
q
If r >> R, Ering
4περ μ
1 q
7.
The electric potential due to a point charge q: V =
8.
9.
The change in the electric potential for a uniform electric field: AV = -E. A
The change in the electric potential for non-uniform electric field: AV = -SE. di
10. The change in electric potential energy: AU = q AV
11. The magnetic field of a moving point charge: B = Ho qvxr
4πT
2
12. The magnetic field due to a current-carrying straight wire:
1
If R >> r, Ering
qr
4π €。 R³
Ho
Bwire =
IL
Но 21
If L≫r (long wire)
Bwire =
4π r√r² + (L/2)²
4π r
13. The magnetic field of a current-carrying coil (A = πR²):
μο
2IAN
Ho 2IAN
B
If r> R B
coil
4π (r² + R2)3/2'
coil
4 π
r3
B center
14. The magnetic field inside a long solenoid:
HONI
B
15. The magnetic field of a bar magnet:
Bmagnet
16.
Ohms' Law: V = IR
17. Electric Power: P = IV
18. Magnetic force on a moving charge: =qx
19. Magnetic force on a current carrying wire due to a uniform magnetic field: F = ILXB
20. Electric flux for a uniform electric field: * = Ē.ĥ A
21. Electric flux for any electric field: = √ Ē.ñ dA
22. Gauss's Law: 6 E. ñ dA = Σinside
Eo
23. Magnetic flux for a uniform magnetic field: += B.nz.
24. Magnetic flux for any magnetic field: += √ B.ñ dA
25. Ampere's Law: $ B. dỉ = HoΣlinside
26. Faraday's Law: emf = -
A mag
At
27. The frequency of the wave:
f = 1/T
28. The angular frequency: v = 2nf
29. The speed of the wave: v = λf
30. Index of refraction: n = c/v
31. Law of refraction (Snell's Law): n₁sine₁ = n₂sine₂
=
Ho 2πIN
4TT
R
Transcribed Image Text:Comprehensive Formula sheet - PHYS 272 1 = k = 9 × 10⁹ 4 περ N. m² C² C² le 1.6 x 10-19 C €8.85 x 10-12 μο T. m² 1 x 10-7 N. m² 4 π C m/s 1. The electric field of a point charge q: 2. The electric force on a charge q: F = qE 3. The electric field at a location on the dipole axis: 4 5. 6. 1 2qsr Eaxis ¯ 4π €。 (r−³)² (r+³)² The electric field at a location perpendicular to the dipole axis: 1 q s E₁ = 4 ΠΕ0 · [r² + (²)²] ³/² 3/2 If r >> s, Eaxis 4 περ 1 2qs r3 1 qs If rs, E₁ 4π € г³ For a location on the perpendicular axis of a uniformly charged rod and at a distance r from the center of the rod, the electric field: 1 9 Erod = If r >> L, Erod 4 περ 2+ r () 1 q 4 π Є。 r² 1 2q/L If Lr, Erod 4 περ I The electric field along the axis of a uniformly charged ring, a distance r from the center of the ring: 1 Ering = qr 4πЄo (R2+2)3/2 1 q If r >> R, Ering 4περ μ 1 q 7. The electric potential due to a point charge q: V = 8. 9. The change in the electric potential for a uniform electric field: AV = -E. A The change in the electric potential for non-uniform electric field: AV = -SE. di 10. The change in electric potential energy: AU = q AV 11. The magnetic field of a moving point charge: B = Ho qvxr 4πT 2 12. The magnetic field due to a current-carrying straight wire: 1 If R >> r, Ering qr 4π €。 R³ Ho Bwire = IL Но 21 If L≫r (long wire) Bwire = 4π r√r² + (L/2)² 4π r 13. The magnetic field of a current-carrying coil (A = πR²): μο 2IAN Ho 2IAN B If r> R B coil 4π (r² + R2)3/2' coil 4 π r3 B center 14. The magnetic field inside a long solenoid: HONI B 15. The magnetic field of a bar magnet: Bmagnet 16. Ohms' Law: V = IR 17. Electric Power: P = IV 18. Magnetic force on a moving charge: =qx 19. Magnetic force on a current carrying wire due to a uniform magnetic field: F = ILXB 20. Electric flux for a uniform electric field: * = Ē.ĥ A 21. Electric flux for any electric field: = √ Ē.ñ dA 22. Gauss's Law: 6 E. ñ dA = Σinside Eo 23. Magnetic flux for a uniform magnetic field: += B.nz. 24. Magnetic flux for any magnetic field: += √ B.ñ dA 25. Ampere's Law: $ B. dỉ = HoΣlinside 26. Faraday's Law: emf = - A mag At 27. The frequency of the wave: f = 1/T 28. The angular frequency: v = 2nf 29. The speed of the wave: v = λf 30. Index of refraction: n = c/v 31. Law of refraction (Snell's Law): n₁sine₁ = n₂sine₂ = Ho 2πIN 4TT R
) A long straight wire suspended in the air carries a conventional current of 5.38 A in the +y direction as shown in Figure (the wire runs along the y axis). At a
particular instant a proton at location (-0.0212, 0, 0) m has velocity (0,-2×105,0) m/s. (Consider the charge of the proton: qp = 1.6×10-19 C).
y
ν
x
+
1. The direction of the magnetic field due to the wire at the location of the proton:
OInto the page
Out of the page
OUpward
ODownward
2. What is the (vector) magnetic field due to the wire at the location of the proton?
=
о
5.075x10^-5
>[T]
3. What is the (vector) magnetic force on the proton due to the current in the wire?
F= < -1.624x10^18
0
0
>[N]
4. Now, consider the proton is moving along -z axis with velocity (0, 0, -2×105) m/s, the magnetic force acting on the proton will be:
=
0
0
[N]
Transcribed Image Text:) A long straight wire suspended in the air carries a conventional current of 5.38 A in the +y direction as shown in Figure (the wire runs along the y axis). At a particular instant a proton at location (-0.0212, 0, 0) m has velocity (0,-2×105,0) m/s. (Consider the charge of the proton: qp = 1.6×10-19 C). y ν x + 1. The direction of the magnetic field due to the wire at the location of the proton: OInto the page Out of the page OUpward ODownward 2. What is the (vector) magnetic field due to the wire at the location of the proton? = о 5.075x10^-5 >[T] 3. What is the (vector) magnetic force on the proton due to the current in the wire? F= < -1.624x10^18 0 0 >[N] 4. Now, consider the proton is moving along -z axis with velocity (0, 0, -2×105) m/s, the magnetic force acting on the proton will be: = 0 0 [N]
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