Question

Uniform magnetic field exists in region given by B=3i+4j+5k . A rod of length 5 m is placed along y - axis is moved along x axis with constant speed 1 m/sec. Then the magnitude of induced e.m.f in the rod is :

• A. zero
• B. 25 volt
• C. 20 volt
• D. 15 volt

Answer 1

Answer: (B)

Given: $\vec{ B }=3 \hat{ i }+4 \hat{ j }+5 \hat{ k }$
Length of rod $\vec{ l }=5 \hat{ j }$
Velocity of rod $\vec{ v }=1 \hat{ i }$
Induced emf is given by $E =(\vec{ v } \times \vec{ B }) \cdot \vec{ l }$
$\therefore E =(1 \hat{ i } \times(3 \hat{ i }+4 \hat{ j }+5 \hat{ k })] \cdot(5 \hat{ j })$
Or $E =(4 \hat{ k }-5 \hat{ j }) \cdot(5 \hat{ j })=-25$ volts
$\vec| E |=25$ volts