Sections 15-18

Question 1

What is the equation for magnetic flux?

Answer 1

ΦB = surface integral of B*dS

Question 2

What is the solenoidal condition?

Answer 2

Flux entering a surface must also exit that surface - closed surface integral of B*dS = 0

Question 3

What is the equation for the force on a charge in a magnetic field?

Answer 3

F = qv X B, where v is the perpendicular velocity and B is the magnetic field strength.

Question 4

What is the larmor radius and how do you get the equation?

Answer 4

Make the force on a charge in a magnetic field equal centripetal acceleration, (m*v^2)/r.

qvB = m*v^2/r, rearrange for r

Question 5

What is the Lorentz force?

Answer 5

qv X B where X is the cross product.

Question 6

How much work is done on a moving charge in a magnetic field?

Answer 6

The magnetic field does no work.

Question 7

What is the force on a section dL of wire? How is this dervied?

Answer 7

dF = IdL X B

• Force on one moving charge in wire is qv X B
• Number density of current carriers n
• Volume of section V = Adl
• So dF = nqvAdl X B = Idl X B

Question 8

What is the force on a crossbar on rails?

Answer 8

F = ILB xhat

Question 9

How do you work out the force on a current loop?

Answer 9

• Side 12: F ~ zhat
• Side 34: Opposite of side 12 - cancels out
• Side 23: Idl X B, with dl = -dl zhat = -IdlB yhat
• Side 41: Idl X B with dl = dl zhat = IdlB yhat

Total force is all of these added up which equals zero.

Question 10

What is the equation for the torque on a current loop?

Answer 10

μ x B where μ= IA sin(ϕ), or NIA sin(ϕ) (magnetic dipole moment), where N is the number of loops

Question 11

What is the permeability of a vacuum and what is its value?

Answer 11

μ0 = 4π*10^−7 H m^−1

Question 12

State the law of Biot-Savert.

Answer 12

B = (μ0/4π)*q*((v(t) X (r-r’(t)))/(|r-r’(t)|^3))

Question 13

What are all the different forces included when two charges move next to each other? What do you do once you’ve worked out the two forces?

Answer 13

Electrostatic force and the lorentz force after working out the magnetic field (law of biot-savert).

You then divide the magnetic force by th electric force and use the equation for the speed of light to simplify.

Question 14

What is the speed of light in terms of μ0 and ϵ0?

Answer 14

1/sqrt(μ0*ϵ0)

Question 15

What is the ration of the magnetic force against the electric force of two charges moving at the same speed parallel to eachother through magnetic and electric fields?

Answer 15

FB/FE = (v/c)^2

Question 16

What is the value of ϵ0?

Answer 16

8.85*10^-12

Question 17

What is Ampere’s Law?

Answer 17

It states that the line integral of a magnetic field around a closed loop is equal to μ0*I(encl).

Question 18

How do you derive the equation for the magnetic field of an infinite straight wire?

Answer 18

• Symmetry - B constant at fixed radius ϱ
• Path C circular and centred on wire along φ (cylindrical coordinates)
• Apply Amperes Law around path C - B and dl have same unit vectors so is just B*dl, and integral of dl is 2pi*ϱ (circumference),
• Enclosed current is I
• 2pi*ϱ*B = μ0*I, rearrange for B

Question 19

What is the equation for the magnetic field of a straight wire?

Answer 19

B= (μ0*I)/(2π*) where ϱ is the distance from the centre of the wire.

Question 20

How do you use Amperes law to find the magnetic field of things?

Answer 20

Similar to Gaussian surface - pick a line integral around the wire with current in, calculate the integral, make it equal to μ0*I(encl) and then do it for different conditions when I(encl) changes.