Test: Electromotive Force - EmSAT Achieve MCQ

• According to Lenz law, the polarity of induced EMF is such that it opposes the change in magnetic flux responsible for its production.
• Magnetic flux depends on the area of the circular conductor. The magnetic flux (ϕ) enclosed by the circular loop can be given as ϕ = B × area
• If the coil is cut somewhere and then moved in and out of the magnetic field, EMF will be generated. 
• The basic cause of induced emf is the change in magnetic flux.
• When a conductor is moved in and out of the magnetic field, magnetic flux across it changes. this causes the generation of EMF in the direction such that it opposes the change. Hence option 4) is correct.

Given: number of spokes, n = 20 length of spokes, l = radius (r) = 1m, magnetic field (B) = 0.4 gauss = 0.4 × 10^-4 tesla, and frequency (f) = 180 rpm = 3 rps

• The relation linear velocity and angular velocity is given by,

⇒ v = rω
Where ω is the angular velocity
Linear velocity of spoke at the axle = 0, and linear velocity at the rim end = rω .

• So the average liner velocity 

• Angular velocity (ω) of the spoke is given as

⇒ ω = 2πf = 2π × 3 = 6π 

• The emf between the axle and rim of the wheel.

⇒ ε = Blv = 0.4 × 10^-4 × 1 × 0.5 × 6π = 3.77× 10^-4 V

• Hence option 4) is correct.

Given, the length of the rod = L, length of the string = 2L, induced emf across the ends of the rod = e 
Then L₁ = 2L, L₂ = 2L + L = 3L
Let the vertical magnetic field in the region is B, then from equation 1, 

Motional emf: The emf induced due to motion relative to a magnetic field is called the motional emf. 

• Consider a straight conductor PQ moving perpendicular to a uniform magnetic field B.
  • Assume the motion of the rod to be uniform with a constant velocity of (v m/s).
  • The rectangle PQRS forms a closed circuit enclosing a changing area due to the motion of the rod PQ.
• The magnetic flux ϕ enclosed by the loop PQRS can be given as:

⇒ ϕ = B × area = B × (l.x)

• Since the conductor is moving, there is a change in the rate of area moving. This causes a rate of change of flux which induces an emf.
• This induced emf is given by:

Where - dx/dt = v is the speed of the conductor PQ​

Electromotive force: The energy per unit electric charge that is imparted by an energy source (battery or electric generator) is called emf or electromotive force.

• Electromotive force is commonly denoted by the acronym emf, EMF or E.
• The SI unit for electromotive force is the volt.
• Electromotive force in a circuit maintains the potential difference.
• Electromotive Force (EMF) makes free electrons to flow in any closed circuit due to difference in electrical pressure or potential. Its unit is Volt.
• Volt is defined as work done per unit charge or energy consumed in bringing a charge from one point to another. 
• So, the Energy per unit charge is electromotive force. 

Since an emf is induced by the change in the magnetic field, there should be a current when there is an emf. Due to this reason, the current inside the coil increases when the magnet is moved inside it.

According to Fleming’s right-hand rule, magnetic flux is pointed by the index finger, motion of the conductor is pointed by the thumb, and induced emf is pointed by the middle finger.

Fleming’s right-hand rule says that the motion of the conductor, the induced emf and the magnetic flux are mutually perpendicular to each other.

Given: number of spokes, n = 20 length of spokes, l = radius (r) = 1m, magnetic field (B) = 0.4 gauss = 0.4 × 10^-4 tesla, and frequency (f) = 180 rpm = 3 rps

The relation linear velocity and angular velocity is given by,

⇒ v = rω

Where ω is the angular velocity

Linear velocity of spoke at the axle = 0, and linear velocity at the rim end = rω .

So the average liner velocity 

Angular velocity (ω) of the spoke is given as
⇒ ω = 2πf = 2π × 3 = 6π 
The emf between the axle and rim of the wheel.
⇒ ε = Blv = 0.4 × 10^-4 × 1 × 0.5 × 6π = 3.77× 10^-4 V
Hence option 4) is correct.

• The EMF induced across the spokes of the ring is the same as the spokes are parallel to each other. So the net EMF will be equal to that generated in a single spoke.
• Hence the number of spokes will not affect the total EMF induced. Hence option 4) is correct.