Solved Examples: Calculating EMF Induced by a Moving Wire

📚 Quick Study Guide

🔍
• The electromotive force (EMF) induced in a moving wire within a magnetic field is given by: $EMF = vBL$, where $v$ is the velocity of the wire, $B$ is the magnetic field strength, and $L$ is the length of the wire.
💡
• The direction of the induced EMF can be determined using the right-hand rule. Point your fingers in the direction of the magnetic field, your thumb in the direction of the wire's motion, and your palm will face the direction of the induced current (and thus the EMF).
📝
• If the wire's motion is not perpendicular to the magnetic field, you'll need to consider the component of the velocity that is perpendicular to the field: $EMF = v_{\perp}BL = vBL\sin(\theta)$, where $\theta$ is the angle between the velocity and the magnetic field.
⚛️
• Remember to use consistent units: velocity in meters per second (m/s), magnetic field in Tesla (T), and length in meters (m), which will give you the EMF in Volts (V).
📊
• For a coil with $N$ turns, the total induced EMF is $N$ times the EMF induced in a single wire: $EMF_{total} = N \cdot EMF$.

Practice Quiz

1. A wire of length 0.5 m moves perpendicularly through a magnetic field of 2 T at a speed of 3 m/s. What is the induced EMF?
1. 0.75 V
2. 1 V
3. 3 V
4. 6 V
2. A 1-meter wire moves at a velocity of 5 m/s through a magnetic field of 0.8 T at an angle of 30 degrees to the field. What is the induced EMF?
1. 2 V
2. 3.46 V
3. 4 V
4. 0 V
3. A coil consists of 100 turns of wire, each 20 cm long, moving at 4 m/s perpendicularly through a 0.5 T magnetic field. What is the total induced EMF?
1. 40 V
2. 20 V
3. 4 V
4. 10 V
4. If the velocity of a wire moving through a magnetic field is doubled, what happens to the induced EMF?
1. It remains the same.
2. It is halved.
3. It is doubled.
4. It is quadrupled.
5. A wire moving parallel to a magnetic field experiences what induced EMF?
1. Maximum EMF
2. Zero EMF
3. Half the maximum EMF
4. It depends on the wire's length.
6. A 0.25 m wire moves at 2 m/s through a magnetic field. If the induced EMF is 0.5 V, what is the magnetic field strength?
1. 0.25 T
2. 0.5 T
3. 1 T
4. 2 T
7. A rectangular coil with 50 turns, each with a length of 30 cm, moves perpendicularly through a 1.2 T magnetic field at 5 m/s. What is the total induced EMF?
1. 90 V
2. 45 V
3. 18 V
4. 0.36 V