A conductor of length 0.5 m moves in a uniform magnetic field of 1.2 T at a velocity of 30 m/s. Find the induced voltage in the conductor when the direction of motion is perpendicular to the field. 

Explanation:

To determine the induced voltage in a conductor moving in a magnetic field, we use the formula for the electromotive force (EMF) induced in a conductor moving through a magnetic field:

EMF (ε) = B × L × v

where:

• B is the magnetic field strength (measured in Tesla, T)
• L is the length of the conductor (measured in meters, m)
• v is the velocity of the conductor (measured in meters per second, m/s)

Given the values:

• B = 1.2 T
• L = 0.5 m
• v = 30 m/s

Substitute these values into the formula:

ε = 1.2 T × 0.5 m × 30 m/s

Perform the multiplication:

ε = 1.2 × 0.5 × 30

ε = 0.6 × 30

ε = 18 V

Therefore, the induced voltage in the conductor is 18 V, which corresponds to Option 2.

Important Information

To further understand the analysis, let’s evaluate the other options:

Option 1: 10 V

This option is incorrect because when you substitute the given values into the formula B × L × v, the result is not 10 V. The correct calculation yields 18 V.

Option 3: 8 V

This option is also incorrect. As shown in the detailed calculation, the product of 1.2 T, 0.5 m, and 30 m/s is 18 V, not 8 V.

Option 4: 15 V

Similarly, this option is incorrect. The induced voltage, according to the given formula and values, is 18 V, not 15 V.

Conclusion:

The correct determination of the induced voltage in a conductor moving in a magnetic field is crucial in understanding electromagnetic principles. In this case, the conductor moving perpendicularly to a magnetic field of 1.2 T at 30 m/s with a length of 0.5 m induces a voltage of 18 V. This induced voltage calculation is pivotal in various applications, including electric generators and motors, where understanding the relationship between magnetic fields and induced EMF is essential for efficient design and operation.