Mod 6

Question 1

Electric field strength formula
Force on charged particle in electric field

Answer 1

E=V/d
F=qE

Question 2

Derive formula for final speed of a charged particle released from rest in magnetic field

Answer 2

W=ΔEk
Fscosθ=ΔEk
qEd=ΔEk E=V/d
qΔV=ΔEk
qΔV=1/2 mv^2f - 1/2mv^2i
vf = sqrt (2qΔV/m)

Question 3

Force on charged particle in magnetic field

Answer 3

F=qvbsinθ
=qb x vsinθ (perpendicular component)

Question 4

How to derive radius of curvature

Answer 4

Fc=Fb
mv^2/r = qvb
r=mv^2/qvb
r=mv/qb

Question 5

Force in motor effect
Force between parallel current carrying conductors

Answer 5

F=nBIlsinθ
F/L = 𝜇o/2π x I1I2/r

Question 6

Magnetic flux equation

Answer 6

Φ=BA cosθ
Φ: magnetic flux (Wb/Tm^-2)
B: magnetic field strength
A: area
θ: angle between magnetic field and normal area

Question 7

State ampere’s law

Answer 7

One ampere of current through each of two parallel conductors of infinite length, separated by one meter in empty space free of other magnetic fields.

Question 8

How can an induced emf be created

Answer 8

By changing the area of the coil
By changing the magnetic field strength within the magnetic field
By changing the orientation of the coil with respect to the direction of the magnetic field.

Question 9

What is faraday’s law
What does the minus mean

Answer 9

Faraday’s experiments showed that the emf induced by a change in magnetic flux depends on the following factors
EMF is directly proportional to the change in flux
EMF is greatest when change in time is smallest
If a coil has N turns, an emf will e produced that is N times greater than for a single coil
𝜀=−𝑁 ΔΦ/Δ𝑡
𝜀: EMF (V)
𝑁: voltage
The minus means that the induced emf always gives rise to a current whose magnetic field always opposes the original change in flux.

Question 10

Importance of lenz’s law

Answer 10

Energy is NOT conserved when the induced emf produces a current with a magnetic field that adds onto the original change in flux.
This will cause the current in the wire to increase, which will then cause the magnetic flux to increase, which will then cause the current to increase again and so on.

Question 11

AC vs DC current

Answer 11

Alternating current describes the flow of charge that changes direction periodically. As a result, the voltage level also reverses along with the current.
Rather than oscillating back and forth, DC provides a constant voltage or current.

Question 12

How do transformers work

Answer 12

Transformers work on the principle of a changing magnetic flux inducing an emf.
Transformers always have 2 coils:
Primary coil
Secondary coil
The changing flux originates with the alternating current supplied to the primary coil.
The changing magnetic flux is directed to the secondary coil where the changing in magnetic flux will also induce an emf in the secondary coil.

Question 13

Difference between step up and step down transformers

Answer 13

Step-up transformers increases the secondary voltage compared to the primary voltage. To do this:
𝑵_𝒔>𝑵_𝒑 then 𝑽_𝒔>𝑽_𝒑
Step-down transformers decreases the secondary voltage compared to the primary voltage. To do this:
𝑵_𝒔<𝑵_𝒑 “ then “ 𝑽_𝒔<𝑽_𝒑

Question 14

Ideal transformer equations

Answer 14

𝑉𝑝/𝑉𝑠 =𝑁𝑝/𝑁𝑠=I𝑠/I𝑝
𝑉𝑝 𝐼𝑝=𝑉𝑠 𝐼𝑠
𝑃=𝑉𝐼
𝑉_𝑝=𝑃𝑟𝑖𝑚𝑎𝑟𝑦 𝑐𝑜𝑖𝑙 𝑣𝑜𝑙𝑡𝑎𝑔𝑒 (𝑉)
𝑉_𝑠=𝑆𝑒𝑐𝑜𝑛𝑑𝑎𝑟𝑦 𝑐𝑜𝑖𝑙 𝑣𝑜𝑙𝑡𝑎𝑔𝑒 (𝑉)
𝑁_𝑝=𝑁𝑜. 𝑜𝑓 𝑐𝑜𝑖𝑙𝑠 𝑖𝑛 𝑝𝑟𝑖𝑚𝑎𝑟𝑦 𝑐𝑜𝑖𝑙
𝑁_𝑠=𝑁𝑜. 𝑜𝑓 𝑐𝑜𝑖𝑙𝑠 𝑖𝑛 𝑠𝑒𝑐𝑜𝑛𝑑𝑎𝑟𝑦 𝑐𝑜𝑖𝑙
𝐼_𝑝=𝐶𝑢𝑟𝑟𝑒𝑛𝑡 𝑖𝑛 𝑝𝑟𝑖𝑚𝑎𝑟𝑦 𝑐𝑜𝑖𝑙 (𝐴)
𝐼_𝑠=𝐶𝑢𝑟𝑟𝑒𝑛𝑡 𝑖𝑛 𝑠𝑒𝑐𝑜𝑛𝑑𝑎𝑟𝑦 𝑐𝑜𝑖𝑙 (𝐴)
𝑃=𝑃𝑜𝑤𝑒𝑟 (𝑊)

Question 15

Problems with power stations

Answer 15

Power stations are usually situated large distances from cities where most of the consumers are located. This presents problems with power losses in the transmission lines. Transmission lines are essentially long metallic conductors that have significant resistance. This means that they have a significant voltage drop across them when they carry a large current. This could result in greatly decreased voltages available to the consumer.

Question 16

How to calculate power loss

Answer 16

Ploss=I^2 x R
Power can be found with P=VI

Question 17

Assess the importance of transformers

Answer 17

To solve transmitting electrical energy at low voltages over large distances, transformers are used to step up the voltage before transmission. If the voltage is increased, the current is reduced.Using transformers enables electricity to be supplied over large distances without wasting too much electrical energy.
If transformers were not used in the power distribution system, either power stations would have to be built in the cities and towns or the users of electricity would have to be located near the power stations. The latter would mean that industries and population centres would have to be located near the energy sources such as hydro-electric dams and coal mines. The former would mean that fossil fuel stations would dump their pollution on the near-by population centres.

Question 18

Torque formula in magnetic field

Answer 18

τ=nIABsinθ
θ: angle between area vector and magnetic field lines

Question 19

How do DC motors operate

Answer 19

DC motors contain a switch assembly (commutator) on the rotating coil shaft that allows the direction of the current through the coil to be reversed every 180˚.
It allows the DC motor to keep rotating because the direction of the current, hence torque, is reversed each half turn by the commutator.
The coils are wound around a soft iron core to increase the magnetic field that passes through them. Arrangement of core and coils is called an armature.
Permanent magnets are usually used to in small motors
Electromagnets are used in larger motors as they produce a larger and stronger magnetic field.
The magnets that are used in DC motors are stationary (stator) and are distinct from the armature (rotating rotor). The commutator is arranged to feed current to the particular coil that is in the best position to provide maximum torque. The total torque will be the sum of the torques on all the individual coils.

Question 20

How do AC motors operate

Answer 20

Majority of electric motors in use rely on AC current. AC induction motors work by producing a rotating magnetic field. The stator is made up of pairs of electromagnets. AC current runs through the coils creating a magnetic field. AC current reverses its polarity. The rotor is made up of a series of conductors (metal bars). As the magnetic field from the stator is rotating (changing magnetic field), an electric current is induced in the conductor of the rotor. Due to Lenz’s law, the rotor will move in the same direction as the changing magnetic field produced by the stator.

Question 21

Pros and cons of AC motors

Answer 21

Advantages of AC motors:
Only have one moving part – the rotor
DC have more moving parts that will wear out and need replacing.
Disadvantage of AC motors:
Speed is fixed at the rate of the AC source (50Hz).

Question 22

How does magnetic braking work

Answer 22

When a conductor moves passed a magnet, eddy currents are induced in the conductor by the magnet (according to Faraday’s law of induction). Due to Lenz’s law, these eddy currents will create their own magnetic field that opposes the original magnetic field of the magnet. This will therefore produce the drag force between the magnet and he conductor, causing the conductor to slow down.

Question 23

Pros and cons of magnetic braking

Answer 23

Advantages of magnetic braking:
Lack of physical contact between components.
Therefore, low maintenance and few replacements.
Disadvantages of magnetic braking:
When there is no motion between the magnet and conductor, there is no static force to keep the conductor at rest.
Therefore, a friction-based braking system is required.

Question 24

How do AC generators function

Answer 24

Generators are construct similarly to motors. The diagram shows a schematic of an ac generator.
Industrial generators usually have the coils stationary and rotate the electromagnet. The principle of inducing an emf is the same. The coil itself may take various shapes, size and positions.
If the output from the coils is transferred to a circuit via continuous slip rings, the alternating current in the coil will be maintained at the output.
Carbon brushes press against the slip rings to allow a constant output to be transferred to a circuit without a fixed point of connection.

Question 25

How do DC generators function

Answer 25

In DC generators, the continuous slip rings in AC generators are replace slip ring commutator.
Ring picking up the output from the coils has two breaks (or splits) in it at opposite sides of the ring
This causes the direction of the output current to change (caused by the commutator) every half turn.
The output will vary from zero to a maximum every half cycle.
DC generators were used to power ancillary equipment in cars. Nowadays, AC generators are used to more commonly as it avoids the problems of wear and sparking across the commutator.

Question 25

What is back emf?
How is it caused
Formula

Answer 25

The back emf generated in a DC motor is the result of current produced in response to the rotation of the rotor inside the motor in the presence of an external magnetic field.
The back emf, following Lenz’s law, opposes the change in the magnetic flux that created it, so this induced emf will be in the opposite direction to the emf creating it. The net emf used by the motor is thus always less that the supplied voltage:
𝜀𝑛𝑒𝑡=𝑉−𝜀𝑏𝑎𝑐𝑘

Question 25

Factors impacting its efficiency

Answer 25

As the motor increases speed, the current induced in it will increase and the back emf will also increase. When a load is applied to the motor, the speed will generally decrease, reducing the back emf and increase the current in the motor.
If the load brings the motor to a sudden halt (example: an electric drill bit gets stuck) the current may be high enough to burn out the motor and the motor windings.
To protect the motor, a resistor is placed in series. It is switched out of the circuit when the current drops below a predetermined level and is switched back into the circuit for protection once the level is exceeded.