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Perpendicular to 85.0 x 10⁻⁵ T magnetic field E = BIV E = BW(5.00x10⁻⁵)(2.0x104) 7.80 x 103 m/s induce electric field the work done on the conductor in moving unit charge from one

Physics

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Answer

6.63 V/m\text{6.63 V/m}

Step-by-step solution

4 steps
  1. Identify the given values.

    The problem describes a conductor moving perpendicular to a magnetic field.

    • Magnetic field strength, B=85.00×10−5 TB = 85.00 \times 10^{-5} \text{ T}
    • Velocity of the conductor, V=7.80×103 m/sV = 7.80 \times 10^3 \text{ m/s}
  2. Determine the quantity to be calculated.

    The student's notes mention "induce electric field" and the formula for motional electromotive force (EMF), ϵ=BlV\epsilon = BlV. Since the length (LL) of the conductor is not provided, we will calculate the induced electric field (EE), which is the EMF per unit length.

  3. Apply the formula for induced electric field.

    When a conductor moves with velocity VV perpendicular to a magnetic field BB, the induced electric field EE within the conductor is given by:

    E=BVE = BV
  4. Substitute the values and calculate.

    Substitute the given values of BB and VV into the formula:

    E=(85.00×10−5 T)×(7.80×103 m/s)E = (85.00 \times 10^{-5} \text{ T}) \times (7.80 \times 10^3 \text{ m/s}) E=(85.00×7.80)×10−5+3 V/mE = (85.00 \times 7.80) \times 10^{-5+3} \text{ V/m} E=663×10−2 V/mE = 663 \times 10^{-2} \text{ V/m} E=6.63 V/mE = 6.63 \text{ V/m}

    The induced electric field is 6.63 V/m\text{6.63 V/m}.

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