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Question

A wire lying along yaxis from y=0 to y=1 m, carries a current of 2 mA in the negative ydirection. 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 (3×104 ^k) N


The wire is lying along yaxis, and the direction of the current is along the negative yaxis.

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=il0[dy^j×(0.3^i+0.4^j)y]


F=i10(0.3ydy)^k

=2×103×0.3×[y22]10 ^k

=3×104 ^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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