# Electromotive Force Problems

• shikagami
In summary, the conversation is discussing various problems related to electromagnetic induction. The answers provided for the first four problems are as follows: 1) a) 5.00 m/s, b) 2.00 Amps, c) 0.960 N; 2) a) 2.00 T, b) point A; 3) a) 3.00 V; 4) a) 0.100 V, b) 0.0125 N. The answers for the remaining problems are not provided and the person is asking for help, particularly with the potential difference problems.

#### shikagami

Here are my homework problems. I did most of them, but I don't understand how to do the others.

1. A rod of length 0.40 m moves in a magnetic field of magnitude B=1.2 T. The emf induced in the moving rod is found to be 2.40 V.
a)what is the speed of the rod?
b)if the total circuit resistance is 1.2 ohms, what is the induced current?
c)What force (magnitude and direction) does the field exert on the rod as a result of this current?

2. A rod of length 0.25 m moves with the constant speed of 6.0 m/s. The induced emf is found to be 3.0 V.
a)what is the magnitude of the magnetic field?
b)If a point called "a" was above a point called "b", which point is at a higher potential?

3. A rod of length 0.15 m moves in a magnetic field directed into the plane of space. If B=0.5 T and the rod moves with the velocity 4 m/s.
a)What is the motional emf induced in the rod?
b)What is the potential difference between the ends of the rod?
c)If a point called "a" was to the right of a point called "b", which point has a higher potential?

4. A conducting rod AB makes contact with metal rails CA and DB. The apparatus is in a uniform magnetic field 0.5 T, perpendicular to the place of the diagram. The rod is 50 cm long.
a)find the magnitude and direction of the emf induced in the rod when it is moving toward the right with a speed 4 m/s.
b)If the resistance of circuit ABDC is 0.2 ohms (assumed constant), find the force required to maintain the rod in motion. Neglect friction.
c)Compare the rate at which mechanical work is done by force (Fv) with the rate of development of heat in the circuit (i^2 R).

5. A coil of 1000 turns enclosing an area of 20cm^2 is rotated from a position where its plane is perpendicular to the Earth's magnetic field to one where its place is parallel to the field, in 0.02 seconds. What average emf is induced if the Earth's magnetic field is 6 x 10^-5 T.

6. A closely wound rectangular coil of 50 turns has dimensions of 12 cm x 25 cm. THe plane of the coil is rotated from a position where it makes an angle of 45 degrees with the magnetic field 2 T to a position perpendicular to the field in time t=0.1 seconds. What is the average emf induced in the coil?

Here are the answers that I got:
1) a) 5.00 m/s b) 2.00 Amps c) .960 N
2) a) 2.00 T b) point A
3) a) 3.00 V b) ? c) ?
4) a) .100 V b) .0125 N c) ?
5) 6.00x10^-3 V
6) 2.55 V

1. A rod of length 0.40 m moves in a magnetic field of magnitude B=1.2 T. The emf induced in the moving rod is found to be 2.40 V.
a)what is the speed of the rod?
b)if the total circuit resistance is 1.2 ohms, what is the induced current?
c)What force (magnitude and direction) does the field exert on the rod as a result of this current?
a)
EMF = dΦ/dt
Φ=BA
=> EMF = BA/t
consider in 1 second, the rod moving at speed v m/s,
the area cut per second = length*v =0.4v

so 2.4 = (1.2*0.4v)/1
v = 5.0 m/s

b)
use EMF = IR

c)
F = BIL
F = 1.2*0.4*2
F = 0.960 N

hth.

Can anyone help me with those other problems that I couldn't get the answers to, especially the potential difference problems.

## 1. What is electromotive force (EMF)?

Electromotive force, also known as EMF, is the measure of the energy that causes electric charges to move through a circuit. It is measured in volts and is the driving force behind the flow of electric current.

## 2. How is EMF different from voltage?

EMF and voltage are often used interchangeably, but they are technically different. Voltage is the potential difference between two points in a circuit, while EMF is the total energy per unit charge that is supplied by the source.

## 3. What are the units of EMF?

The units of EMF are volts (V). This is because EMF is a measure of energy per unit charge, and energy is typically measured in joules (J) and charge is measured in coulombs (C). Therefore, volts (V) can be expressed as J/C.

## 4. How is EMF calculated in a circuit?

EMF can be calculated using the equation EMF = I x R, where I is the current in amperes (A) and R is the resistance in ohms (Ω). This equation is derived from Ohm's Law, which states that voltage is equal to current multiplied by resistance.

## 5. What factors affect EMF in a circuit?

Several factors can affect EMF in a circuit, including the type of source (such as a battery or generator), the number of cells or coils in the source, and the type of material used in the source. Additionally, the resistance of the circuit and the temperature can also impact the EMF.

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