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Question
A copper wire of length 2 m is placed in the magnetic field, →B=(2^i+4^j) T along z−axis. It moves with velocity, →v=(4^i+6^j+8^k) m/s. Calculate the dynamic emf across its ends.
A copper wire of length 2 m is placed in the magnetic field, →B=(2^i+4^j) T along z−axis. It moves with velocity, →v=(4^i+6^j+8^k) m/s. Calculate the dynamic emf across its ends.
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Solution
The correct option is D 8 V
Given:
Length of wire, →l=(2^k) m
Magnetic field, →B=(2^i+4^j) T
Velocity of wire, →v=(4^i+6^j+8^k) m/s
EMF induced across the ends of wire,
ΔV=(→v×→B).→l
⇒ΔV=∣∣
∣
∣∣^i^j^k468240∣∣
∣
∣∣.(2^k)
⇒ΔV=[^i(0−32)−^j(0−16)+^k(16−12)].(2^k)
⇒ΔV=[−32^i+16^j+4^k].(2^k)
⇒ΔV=8 V
Given:
Length of wire, →l=(2^k) m
Magnetic field, →B=(2^i+4^j) T
Velocity of wire, →v=(4^i+6^j+8^k) m/s
EMF induced across the ends of wire,
ΔV=(→v×→B).→l
⇒ΔV=∣∣ ∣ ∣∣^i^j^k468240∣∣ ∣ ∣∣.(2^k)
⇒ΔV=[^i(0−32)−^j(0−16)+^k(16−12)].(2^k)
⇒ΔV=[−32^i+16^j+4^k].(2^k)
⇒ΔV=8 V
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