A Long Vertical Wire Carries a Steady $70 \mathrm {~A}$ Current as Shown in the Figure, a Pair of Horizontal

question 64

Multiple Choice

A long vertical wire carries a steady $70 \mathrm {~A}$ current. As shown in the figure, a pair of horizontal rails are $0.20 \mathrm {~m}$ apart. $\mathbf { A } 20 - \Omega$ resistor connects points $a$ and $b$ , at the end of the rails. $\mathbf { A }$ bar is in contact with the rails, and is moved by an external force with a constant horizontal velocity of $0.90 \mathrm {~m} / \mathrm { s }$ to the right, as shown. The bar and the rails have negligible resistance. At the instant that the bar is $0.20 \mathrm {~m}$ from the wire, what are the induced current in the resistor and its direction through the resistor? $\left( \mu _ { 0 } = 4 \pi \times 10 ^ { - 7 } \mathrm {~T} \cdot \mathrm { m } / \mathrm { A } \right)$

• A) \(0.63 \mu \mathrm { A }\), from \(b\) to \(a\)
• B) \(0.32 \mu \mathrm { A }\), from \(b\) to \(a\)
• C) \(1.9 \mu \mathrm { A }\), from \(b\) to \(a\)
• D) \(0.32 \mu \mathrm { A }\), from \(a\) to \(b\)
• E) \(0.63 \mu \mathrm { A }\), from \(a\) to \(b\)

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Definitions:

Inference Forms

Patterns or structures of logical reasoning that derive conclusions from premises based on rules.

MP

An abbreviation for Modus Ponens, a form of argument in logic where if a conditional statement ("if P, then Q") is accepted, and the antecedent P holds, then the consequent Q logically must also hold.

MT

An abbreviation often referring to Modus Tollens, a form of deductive argument where the consequent in a conditional proposition is negated, leading to the negation of the antecedent.

Simp

Slang for a person who overly defers to someone else, typically a man excessively reverent or submissive towards a woman.