Question

A conductor is moving with a speed of $10 \text{ m/s}$ in the direction perpendicular to the direction of magnetic field of induction $0.8 \text{ T}$. If it induces an E.M.F. of $8 \text{ V}$ between the ends of the conductor, the length of the conductor is \dots

• A. $1 \text{ m}$
• B. $2 \text{ m}$
• C. $3 \text{ m}$
• D. $4 \text{ m}$

Hint:

Motional E.M.F. becomes maximum when the conductor moves perpendicular to the magnetic field.

Answer 1

The Correct Option is A

Concept: When a conductor moves through a magnetic field, an E.M.F. is induced across its ends due to electromagnetic induction. The formula for motional E.M.F. is: \[ \varepsilon = Blv \] Where:
• $\varepsilon$ = induced E.M.F.
• $B$ = magnetic field induction
• $l$ = length of conductor
• $v$ = velocity of conductor

Step 1: Write the given values. \[ \varepsilon = 8 \text{ V} \] \[ B = 0.8 \text{ T} \] \[ v = 10 \text{ m/s} \]

Step 2: Substitute into the formula. \[ 8 = 0.8 \times l \times 10 \] \[ 8 = 8l \]

Step 3: Solve for $l$. \[ l = \frac{8}{8} \] \[ l = 1 \text{ m} \] Hence, the length of the conductor is: \[ 1 \text{ m} \]