A metal sample carrying a current along X- axis with density J_ x is subjected to a magnetic field B_z (along z- axis). The electric field E_ y developed along Y -axis is directly proportional to J_ x as well as B_ z .

Correct answer: B. (m^3)/(A s) According to question E_ y J_ x B_ Z Constant of proportionality K= E_ y B_ Z J_ x = C J_ x = m^3 As [. As (E)/(B)=C (speed of light) and .J= I Area ]

JEE Main 201325 AprilOnline

Exam: JEE Main
Year: 2013
Date: 25 April
Mode: Online
Subject: Physics
Chapter: Electromagnetic Induction

JEE Main 2013 · 25 April · Online · Physics · Electromagnetic Induction

A metal sample carrying a current along X- axis with density J_ x...

A metal sample carrying a current along

\mathrm{X-}

axis with density

\mathrm{J}_{\mathrm{x}}

is subjected to a magnetic field

\mathrm{B}_z

(along

\mathrm{z-}

axis). The electric field

\mathrm{E}_{\mathrm{y}}

developed along

\mathrm{Y}

-axis is directly proportional to

\mathrm{J}_{\mathrm{x}}

as well as

\mathrm{B}_{\mathrm{z}}

. The constant of proportionality has SI unit.

Options

A $\frac{m^2}{A}$
B $\frac{m^3}{A s}$
C $\frac{m^2}{A s}$
D $\frac{A s}{m^3}$

Correct answer

B. $\frac{m^3}{A s}$

Step-by-step solution

According to question

\mathrm{E}_{\mathrm{y}} \propto \mathrm{J}_{\mathrm{x}} \mathrm{B}_{\mathrm{Z}} \therefore

Constant of proportionality

\mathrm{K}=\frac{\mathrm{E}_{\mathrm{y}}}{\mathrm{B}_{\mathrm{Z}} \mathrm{J}_{\mathrm{x}}}=\frac{\mathrm{C}}{\mathrm{J}_{\mathrm{x}}}=\frac{\mathrm{m}^3}{\mathrm{As}} \left[\right.

\frac{E}{B}=C

(speed of light) and \left.J=\frac{I}{\text{ Area }}\right]

Practice Electromagnetic Induction on Quantrex Academy →

More from Electromagnetic Induction

List-I contains four conducting loops lying in the XY plane, as shown in the figures. The… JEE Advanced 2026 A 30 cm long solenoid has 10 turns per cm and area of 5 cm ^2 . The current through the… JEE Main 2026 A square loop of side 2 cm is placed in a time varying magnetic field with magnitude as B… JEE Main 2026 An inductor of inductance 10 mH having resistance of 100\,Ω is connected to battery of… JEE Main 2026 A metal rod of length L rotates about one end at origin with a uniform angular velocity ω… JEE Main 2026 A circular loop of radius 20 cm and resistance 2\ Ω is placed in a time varying magnetic… JEE Main 2026 In the given circuit below inductance values of L_1 , L_2 and L_3 are same. The magnetic… JEE Main 2026 A circular current loop of radius R is placed inside square loop of side length L (L >>… JEE Main 2026 Full Electromagnetic Induction list All JEE Main PYQs