A conductor of length 1m moves with a velocity of 50 ms^ -1 at an angle of 30o to the direction of a uniform…

Analyze the question

A straight conductor moving through a magnetic field cuts the field lines and has an e.m.f. induced in it. We're given:

• Length, L = 1 m
• Velocity, v = 50 m/s
• Angle between velocity and field, θ = 30°
• Flux density, B = 1.5 Wb/m² (1.5 T)

Concept

The motional e.m.f. in a conductor is:

E = B L v sin θ

Only the component of velocity perpendicular to the field, v sin θ, cuts the flux lines and produces the e.m.f.

Solution

E = B L v sin θ E = 1.5 × 1 × 50 × sin 30°

Since sin 30° = 0.5:

E = 1.5 × 1 × 50 × 0.5 E = 75 × 0.5 E = 37.5 V

Answer

The induced e.m.f. is 37.5 V, which matches option A.

Exam tip

Many students forget the sin θ and stop at 75 V, which is option C, a trap answer. Always check the angle. If the angle is given between the velocity and the field (not the plane), use sin θ. Useful values to memorise: sin 30° = 0.5, sin 45° ≈ 0.707, sin 60° ≈ 0.866.