A horizontal straight wire 5 m long extending from east to west falling freely at right angle to horizontal component of earth's magnetic field $0.60 \times 10^{-4} \mathrm{Wbm}^{-2}$. The instantaneous value of emf induced in the wire when its velocity is $10 \mathrm{~ms}^{-1}$ is ______ $\times 10^{-3} \mathrm{~V}$.

JEE Main · 2024 · 29 Jan 2024 · Shift 2 · Electromagnetic Induction

A horizontal straight wire 5 m long extending from east to west falling freely at right angle to horizontal component of earth's magnetic field

0.60 \times 1 0^{- 4} Wbm^{- 2}

. The instantaneous value of emf induced in the wire when its velocity is

10 ms^{- 1}

is ______

\times 1 0^{- 3} V

Answer: 3

Solution

The wire falls freely, so its velocity is vertical while the wire itself is horizontal and perpendicular to the horizontal component of Earth's magnetic field

B_{H}

— exactly the condition for motional emf:

e = B_{H} v ℓ = 0.60 \times 1 0^{- 4} \times 10 \times 5 = 3 \times 1 0^{- 3} V

The required value is 3.

JEE Main · 2024 · 29 Jan 2024 · Shift 2 · Integer answer

Practise more: all JEE Main PYQs on Electromagnetic Induction →

More JEE Main questions on Electromagnetic Induction

XPQY is a vertical smooth long loop having a total resistance R where PX is parallel to QY and separation between them is $l$ . A constant magnetic field B perpendicular to the plane of the loop exists in the entire space. A rod CD of length L ( $L > l$ ) and mass $m$ is made to sli …
JEE Main 2026View solution →
Three identical coils $C_{1}, C_{2}$ and $C_{3}$ are closely placed such that they share a common axis. $C_{2}$ is exactly midway. $C_{1}$ carries current $I$ in anti-clockwise direction while $C_{3}$ carries curre …
JEE Main 2026View solution →
Inductance of a coil with $1 0^{4}$ turns is 10 mH and it is connected to a dc source of 10 V with internal resistance of $10Ω$ . The energy density in the inductor when the current reaches $(\frac{1}{e})$ of its maximum value is …
JEE Main 2026View solution →
Figure shows the circuit that contains three resistances ( $9Ω$ each) and two inductors (4 mH each). The reading of ammeter at the moment switch $K$ is turned ON, is ______ A.
JEE Main 2026View solution →
A conducting circular loop is rotated about its diameter at a constant angular speed of $100 rad / s$ in a magnetic field of 0.5 T perpendicular to the axis of rotation. When the loop is rotated by $3 0^{\circ}$ from the horizontal position, the induced EMF is 15 …
JEE Main 2026View solution →
A capacitor C is first charged fully with potential difference of $V_{0}$ and disconnected from the battery. The charged capacitor is connected across an inductor having inductance L . In t s $25%$ of the initial energy in the capacitor is transferred to the induct …
JEE Main 2026View solution →