JEE Main · 2024 · 05 Apr 2024 · Shift 1 · Magnetic Effects of Current

A 2A current carrying straight metal wire of resistance

1Ω

, resistivity

2 \times 1 0^{- 6} Ω m

, area of cross-section

10 mm^{2}

and mass 500 g is suspended horizontally in mid air by applying a uniform magnetic field

B

. The magnitude of B is ______

\times 1 0^{- 1} T

(given,

g = 10 m / s^{2}

)

Answer: 5

Solution

From

R = \frac{ρ L}{A}

the wire length is

L = \frac{R A}{ρ} = \frac{( 1 ) ( 10 \times 1 0 ^{- 6} )}{2 \times 1 0 ^{- 6}} = 5 m .

For equilibrium the magnetic force balances gravity,

B i L = m g

B = \frac{m g}{i L} = \frac{0.5 \times 10}{2 \times 5} = 0.5 T = 5 \times 1 0^{- 1} T .

Hence the answer is

5

JEE Main · 2024 · 05 Apr 2024 · Shift 1 · Integer answer

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