A metallic rod of length 2 m (aligned along y-axis) is moving with velocity 3 m/s directed along positive x-axis. If a
uniform magnetic field B = (21-3j) T exists in the region. The induced emf in the rod will be
18 V
10 V
5 V
Zero
Answers
Answer:
Concept:
The component of the velocity perpendicular to the magnetic field produces a magnetic force perpendicular to both this velocity and the field: v perp = v sin θ, v para = v cos θ. v perp = v sin θ , v para = v cos θ . where θ is the angle between v and B
Explanation:
Given:
A metallic rod of length 2 m
Velocity 3 m/s
Uniform magnetic field B = (21-3j) T
Find:
The induced emf in the rod
Solution:
An emf induced by motion relative to a magnetic field is called a motional emf. This is represented by the equation emf = LvB, where L is the length of the object moving at speed v relative to the strength of the magnetic field B.
emf = 2m × 3m/s × (21-3j) T
emf = 2 ×3 ×-3(j-7)
emf = 18 V
Option (A) = 18V is correct.
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Concept:
Motional emf can be defined as the emf induced by motion relative to a magnetic field.
emf can be represented by the equation,
emf = (B×v)L
where L is the length of the object, v is the velocity of the object and B is the magnetic field.
Given:
Length of rod, L = 2j m (in y-axis)
Velocity, v = 3i m/s (in x-axis)
Magnetic field, B = (2i-3j) T
Find:
The induced emf in the rod.
Solution:
emf = (B×v)L
where L is the length of the object, v is the velocity of the object and B is the magnetic field.
Substituting the values,
emf = (3i m/s × (2i-3j) T) 2j m
emf = (-9k)·(2j)
emf = 0 V
Hence, the induced emf is 0 V. Hence, the correct option is (D) Zero.
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