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Question

# A conductor lies along the z - axis at −1.5≤z<1.5 m and carries a fixed current of 10.0 A in −^az direction (see figure). For a field →B=3.0×10−4e−0.2x^ay T , find the power required to move the conductor at constant speed to x=2.0 m,y=0 m in 5×10−3 s. Assume parallel motion along the x - axis.

A
29.7 W
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B
14.85 W
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C
2.97 W
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D
1.57 W
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Solution

## The correct option is C 2.97 W Given: i=10 A, →B=3.0×10−4e−0.2x^ay T , x=2.0 m,y=0 m in t=5×10−3 s. Work done in moving the conductor is, W=∫20Fext.dx=∫20B(x)IL.dx Required power, P=Work donetime P=1t∫20Fext.dx=1t∫20B(x)ILdx=15×10−3∫203×10−4e−0.2x×10×3dx =9[1−e−0.4] =9[1−1e0.4]=2.96 W Hence, option (B) is correct.

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