Question

# A wire lying along y−axis from y=0 to y=1 m, carries a current of 2 mA in the negative y−direction. The wire lies in a non-uniform magnetic field given by, →B=(0.3y ^i+0.4y ^j) T. The magnetic force on the entire wire will be -

A
(6×103 ^k) N
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B
(6×103 ^k) N
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C
(3×104 ^k) N
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D
(3×104 ^k) N
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Solution

## The correct option is D (3×10−4 ^k) N The wire is lying along y−axis, and the direction of the current is along the negative y−axis. Let us consider an element of length dy, at a distance y, from the origin and on the y axis. ∴→dl=−dy^j Magnetic force on the current carrying conductor element is, −→dF=i(→dl×→B) Now, magnetic force on the entire conductor, →F=∫i(→dl×→B) ∴→F=−i∫l0[dy^j×(0.3^i+0.4^j)y] ⇒→F=−i∫10(−0.3ydy)^k =2×10−3×0.3×[y22]10 ^k =3×10−4 ^k N <!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Hence, option (D) is the correct answer. Why this question? This question has been asked to make you understand the concept of force experienced by a current carrying conductor in a magnetic field.

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