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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=(0.3T/m)y^i+(0.4Tm)y^j.The magnetic force on the entire wire is

A
3×104^jN
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B
6×103^kN
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C
3×104^kN
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D
3×104^kN
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Solution

## The correct option is C 3×10−4^kNDue to ^j component of →B, magnetic force is zero.It is only due to ^i component.→l is towards -y direction →B is towards ^i direction.Hence →l×→B (the direction of magnetic force is +ve -Z) F=∫dF=∫10(i)(dy)(B) =∫10(2×10−3)dy(0.3y) =3×10−4N

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