A conducting rod of length 1 m aligned along the unit vector ( 5 3 j ^ + 5 4 k ^ ) is moving with a velocity v = ( 2 i ^ ) m/s. The motion take place in a uniform magnetic field B = ( j ^ − 2 k ^ ) tesla. Find the magnitude of induced emf across the rod in volt.

Use the scalar triple product. E = ∣ ( v × B ) ⋅ ℓ ∣ v × B = 2 i ^ × ( j ^ − 2 k ^ ) = 4 j ^ + 2 k ^ ℓ = 5 3 j ^ + 5 4 k ^ E = 4 5 3 + 2 5 4 = 4 V Answer 4.

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Physics - EMI/AC Question with Solution | TestHub

PhysicsEMI/ACMotional & Rotational EMFMedium2 minQB

PhysicsMediuminteger

A conducting rod of length 1 m aligned along the unit vector $(\frac{3}{5} \hat{j} + \frac{4}{5} \hat{k})$ is moving with a velocity $v = (2 \hat{i})$ m/s. The motion take place in a uniform magnetic field $B = (\hat{j} - 2 \hat{k})$ tesla. Find the magnitude of induced emf across the rod in volt.

Answer:

Solution:

Use the scalar triple product.

$E = ∣ (v \times B) \cdot ℓ ∣$

$v \times B = 2 \hat{i} \times (\hat{j} - 2 \hat{k}) = 4 \hat{j} + 2 \hat{k}$

$ℓ = \frac{3}{5} \hat{j} + \frac{4}{5} \hat{k}$

$E = 4 \frac{3}{5} + 2 \frac{4}{5} = 4 V$

Answer 4.

Stream:JEESubject:PhysicsTopic:EMI/ACSubtopic:Motional & Rotational EMF

⏱ 2mℹ️ Source: QB

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