Electromagnetism equations

Question 1

For two wires in parallel what is the relationship between force, currents, length and distance between(a)

Answer 1

F = 𝜇0𝜇𝑟 𝐼1𝐼2𝑙/2𝜋a

Question 2

What is 𝜇0 and 𝜇𝑟?

Answer 2

𝜇0: Permeability of free space (4𝜋×10−7 N/A^2)

𝜇𝑟: Relative permeability of surrounding material (=1 for free space)

Question 3

If currents in two wires have the same polarity what can be said about the force?

Answer 3

It is attractive and positive.

Question 4

If currents in two wires have opposite polarity what can be said about the force?

Answer 4

It is repulsive and negative.

Question 5

What links Force, Magnetic flux density, current and length?

Answer 5

F = BI𝑙 sinθ

Current is the one in the field not setting up the field

Question 6

What links B, I setting up field, a and 𝜇0

Answer 6

B = 𝜇0 I/2𝜋a

Question 7

How are magnetic flux density and field strength related?

Answer 7

𝐵 = 𝜇0𝜇𝑟𝐻

Question 8

What links H, I setting up field and a?

Answer 8

H = I/2𝜋a

Question 9

What links H, I and 𝑙?

Answer 9

𝐹 = 𝜇0 𝐻𝐼𝑙

Question 10

Name parts of Fleming’s left hand rule

Answer 10

Thumb - Force
First Finger - Field
SeCond finger - Current

Question 11

What is Ampere’s Law in words?

Answer 11

The integral of magnetic field strength round a closed path is equal to the current enclosed

Question 12

What is Ampere’s Law in full and if H is constant

Answer 12

-∮ 𝐻⃗ 𝑑𝑙 = ∑𝐼𝑒𝑛c

-∑𝐻𝑡 Δ𝑙 = ∑𝐼𝑒𝑛c
Ht is tangential component of H.

Question 13

Simplify Ampere’s Law for a long straight solenoid

Answer 13

• Field uniform inside and 0 outside.
• H = nI
• B = 𝜇0 nI

Question 14

Simplify Ampere’s Law for a Long solenoid (toroid)

Answer 14

• Uniform in winding, radius of coil < radius of toroid
• H = NI/2𝜋a
• B = 𝜇0 NI/2𝜋a

Question 15

What links Magnetic flux, flux density and area?

Answer 15

Φ(Wb) = 𝐵𝐴 sin θ

Question 16

Describe B-H curves for toroid’s of magnetic and non-magnetic materials.

Answer 16

• Non-magnetic is linear relationship with grad 𝜇0.

- Magnetic has non linear and relative permeability changes with H.

Question 17

State 4 points of a hysteresis curve.

Answer 17

1. B is a non-linear function of H.
2. B lags behind H (displaying hysteresis).
3. When H=0 the remaining B is remanence, Br.
4. The H value for B=0 is coercivity, Hc

Question 18

What is saturation in B-H curves?

Answer 18

When the gradient reduces. It is not a good use of energy.

Question 19

What is an equation for energy loss in hysteresis

Answer 19

𝑃 ℎ𝑦𝑠 ∝ 𝐴 f

Question 20

What does the size of B-H loop mean?

Answer 20

Small = soft magnetic material.
Large = hard magnetic material

Question 21

What links MMF(Magnetomotive force), number of turns and current?

Answer 21

F = NI

Question 22

What links reluctance, Area, 𝜇0, 𝜇r and length?

Answer 22

Reluctance = L/(A 𝜇0 𝜇r)

Question 23

What links MMF, Reluctance and flux?

Answer 23

MMF = Reluctance x Flux

Question 24

What is the relationship for reluctance in parallel? Give a reason this equation isn’t entirely true

Answer 24

1/Rt = 1/R1 + 1/R2 (acts same as parallel resistors). -Some flux lost to leakage flux so not entirely true

Question 25

What is the relationship for reluctance over an air gap (series circuit) of toroid?`

Answer 25

Rtotal = Rgap + Rcore

Question 26

What is true about magnetic flux at a juncton?

Answer 26

It sums to zero

Question 27

What do electrical and magnetic circuits have in common?

Answer 27

All circuit analysis rules apply to both, EMF = MMF, Reluctance = Resistance, Current = Flux (These pairs do same job in either electrical or magnetic)

Question 28

What is Lenz’s Law

Answer 28

EMF proportional to -𝑑𝜙/𝑑t

Question 29

What links magnetic flux linkage, number of turns and magnetic flux?

Answer 29

Ψ = 𝑁𝜙

Question 30

What is Faraday’s Law fully defined?

Answer 30

𝑒 = −𝑁 𝑑𝜙/𝑑𝑡 = −𝑑Ψ/𝑑t

Question 31

State 3 facts from Faraday’s Law

Answer 31

 No EMF is induced if there is no relative movement between the field and the conductors.
 An EMF is induced NOT a current. Current only flows as a result of the EMF and if the circuit is closed.
 Any current flowing acts to oppose the field that created it so will produce an opposing magnetic field of its own. This is the fundamental principle behind motors and generators.

Question 32

For a generator what links EMF, 𝐵, 𝑙, 𝑣

Answer 32

𝑒 = −𝐵𝑙𝑣, for closed circuit both current can be found by dividing both sides by resistance

Question 33

What is Fleming’s Right Hand rule?

Answer 33

For generators, Thumb motion, First Field, Second Current. Different to left hand rule as for induction there is a minus in Lenz’s law.

Question 34

What are 3 ways of inducing emf?

Answer 34

1. Change flux density EMF = −𝑁𝐵̂𝐴𝜔 cos 𝜔𝑡
2. Change coil orientation with constant field.
3. Varying field and conductors move through

Question 35

What links Force, Magnetic Flux density, Current and length?

What links Lorentz Force, charge, E, B and velocity?

Answer 35

F = B I L, F = q(E+vxB)

Question 36

How can you derive Lorentz force for emf?

Answer 36

Divide by q and integrate with respect to length

Question 37

What is self inductance, L, and a equation to define it using current and flux linkage?

Answer 37

The ability of a coil to store energy in a magnetic field. Ψ = Li, Inductance(L) in Henry

Question 38

What is the equation for leakage flux?

Answer 38

L(leak) = Ψ(leak)/i

Question 39

What links flux, number of turns, current and reluctance

Answer 39

𝜙 = Ni/Reluctance

Question 40

Equation of mutual flux linkage?

Answer 40

Ψ𝐴𝐵 = 𝑁B x 𝜙AB - depends on turns on output B

Question 41

Equation of mutual inductance?

Answer 41

M(AB) = Ψ(𝐴𝐵) / i(A) - depends on driving current

Question 42

How can we find emf using mutual inductance or mutual linkage? With A as driving current coil and B as excited coil

Answer 42

𝑒(𝐵) = −𝑀(𝐴𝐵) x 𝑑𝑖(𝐴) /𝑑t or 𝑒(𝐵) = −𝑑Ψ(𝐴𝐵) /𝑑𝑡

Question 43

Equation for self inductance

Answer 43

L = Ψ/i = 𝜇0𝜇𝑟𝑁^2𝐴 / 2𝜋r

Question 44

What links Mutual inductance and self inductance and coupling coefficient?

Answer 44

M(AB) = k√𝐿(𝐴)𝐿(B)

Question 45

What links, energy stored in inductor, inductance and current

Answer 45

E = 1/2 LI^2