A wire of length 10 cm translates in a direction that makes an angle of 60^ with its length. The plane of motion is perpendicular to a uniform magnetic field of 1.0 T present in the region. Determine the emf induced between the ends of the wire if its speed of translation is 20 cm s ⁻¹ .

Step-by-step solution

Given: Length of the wire, l = 10 cm = 0.1 m Speed of translation, v = 20 cm s ⁻¹ = 0.2 m s ⁻¹ Magnetic field, B = 1.0 T Angle between velocity and length of the wire, = 60^ The motional emf induced in a straight conductor moving in a uniform magnetic field is given by the scalar triple product = |( v B ) l | . Since v and l are in a plane perpendicular to B , this simplifies to: = B v l Substituting the given values: = 1.0 0.2 0.1 60^ = 0.02 3 2 = 0.01 1.732 0.017 V