Question:
A wire of length 20 cm is moving with a velocity of 180 m/min perpendicular to a magnetic field. If the induced emf in the wire is 3 V, the magnitude of the field in tesla is:
A wire of length 20 cm is moving with a velocity of 180 m/min perpendicular to a magnetic field. If the induced emf in the wire is 3 V, the magnitude of the field in tesla is:
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Induced emf in a moving conductor is proportional to \(B\), length, and velocity: \(\mathcal{E} = B L v\).
Updated On: Jul 18, 2026
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The Correct Option is C
Solution and Explanation
Step 1: Formula for induced emf.
When a conductor of length \(L\) moves perpendicular to a magnetic field \(B\) with velocity \(v\), the induced emf is: \[ \mathcal{E} = B L v \]
Step 2: Converting units.
Given velocity \(v = 180 \, m/min = 180/60 = 3 \, m/s\). Length of wire \(L = 20 \, cm = 0.2 \, m\).
Step 3: Substituting values.
\[ 3 = B \cdot 0.2 \cdot 3 \]
Step 4: Solving for magnetic field.
\[ B = \frac{3}{0.6} = 5 \, T \]
Step 5: Verification.
\(\mathcal{E} = 5 \cdot 0.2 \cdot 3 = 3\, V\) ✓
Step 6: Final conclusion.
\[ \boxed{5 \, T} \]
When a conductor of length \(L\) moves perpendicular to a magnetic field \(B\) with velocity \(v\), the induced emf is: \[ \mathcal{E} = B L v \]
Step 2: Converting units.
Given velocity \(v = 180 \, m/min = 180/60 = 3 \, m/s\). Length of wire \(L = 20 \, cm = 0.2 \, m\).
Step 3: Substituting values.
\[ 3 = B \cdot 0.2 \cdot 3 \]
Step 4: Solving for magnetic field.
\[ B = \frac{3}{0.6} = 5 \, T \]
Step 5: Verification.
\(\mathcal{E} = 5 \cdot 0.2 \cdot 3 = 3\, V\) ✓
Step 6: Final conclusion.
\[ \boxed{5 \, T} \]
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