A potential difference of 55*10^(-4) Volt is produced across the terminals of a second hand of a clock due to a magnetic field perpendicular to it. Given that length of second hand is 50 cm , calculate magnetic flux density acting on it .
This is How I tackled the problem
Angular vel.= 2pi / 60 sec. (since it completes one cycle in 60 sec)
linear vel. = omega * rad. = 2pi/60 * (0.5)
Blv sin90=Epsilon=E.m.f
Then , B=Epsilon/(length hand * linear vel)=0.21 T

To find the magnetic flux density acting on the second hand of a clock, we can indeed use the relationship between electromotive force (E.m.f.), magnetic field strength (B), the length of the conductor (in this case, the second hand), and its linear velocity. Let's break down the problem step by step to ensure clarity and understanding.

Understanding the Problem

We are given a potential difference (E.m.f.) of 55 x 10^-4 Volts across the terminals of the second hand, which is 50 cm long. The magnetic field is perpendicular to the motion of the second hand. Our goal is to calculate the magnetic flux density (B).

Step 1: Convert Units

First, we need to convert the length of the second hand from centimeters to meters for consistency in SI units:

• Length of the second hand, L = 50 cm = 0.5 m

Step 2: Calculate Angular Velocity

The second hand completes one full rotation (2π radians) in 60 seconds. Therefore, the angular velocity (ω) can be calculated as:

• ω = 2π / 60 rad/s

Step 3: Determine Linear Velocity

The linear velocity (v) of the end of the second hand can be found using the formula:

• v = ω × r
• Here, r is the radius, which is the length of the second hand (0.5 m).

Substituting the values:

• v = (2π / 60) × 0.5
• v ≈ 0.05236 m/s

Step 4: Apply the Formula for E.m.f.

The formula relating E.m.f. (ε), magnetic flux density (B), length of the conductor (L), and linear velocity (v) is given by:

• ε = B × L × v × sin(θ)

Since the magnetic field is perpendicular to the motion of the second hand, sin(θ) = sin(90°) = 1. Thus, the equation simplifies to:

• ε = B × L × v

Step 5: Solve for Magnetic Flux Density (B)

Rearranging the equation to solve for B gives us:

• B = ε / (L × v)

Now, substituting the known values:

• ε = 55 x 10^-4 V
• L = 0.5 m
• v ≈ 0.05236 m/s

Calculating B:

• B = (55 x 10^-4) / (0.5 × 0.05236)
• B ≈ 0.21 T

Final Result

The magnetic flux density acting on the second hand of the clock is approximately 0.21 Tesla. This value indicates the strength of the magnetic field that induces the potential difference across the second hand as it moves through the magnetic field.