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Question

# A uniform magnetic field →B=Bo^k exists in a region . A current carrying wire is placed in x−y plane as shown in the figure. The magnetic force acting on the part AB of wire is:

A
2Boia ^i
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B
3Boia ^j
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C
3Boia ^k
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D
Boia ^j
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Solution

## The correct option is B −3Boia ^jThe wire AB consists of five straight sections i.e AC,CD,DE,EF and FB as shown in the figure. However, if we look at the wire AB and the overall direction of curent, the effective length vector is →LAB as shown below Thus, →LAB=3a^i Now, →F=i(→LAB×→B) →F=i(3a^i×Bo^k) (∵^i×^k=−^j) →F=−3Boai ^j Hence, option (B) is the correct answer.

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