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A charge of 3 imes 10⁻⁶ C moves with a velocity of 2 imes 105 m/s perpendicular to a magnetic field of 0.5 T. Calculate the magnetic force on the charge.

Physics

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Answer

0.3 N\text{0.3 N}

Step-by-step solution

4 steps
  1. Identify the given values.

    The charge is q=3×10−6q = 3 \times 10^{-6} C.
    The velocity is v=2×105v = 2 \times 10^5 m/s. (Note: The unit in the question, m/s2^2, is typically for acceleration. We will proceed assuming it's m/s for velocity, which is standard for this type of problem.)
    The magnetic field strength is B=0.5B = 0.5 T.
    The charge moves perpendicular to the magnetic field, so the angle θ=90∘\theta = 90^\circ.

  2. State the formula for magnetic force on a moving charge.

    The magnetic force FF acting on a charge qq moving with velocity vv in a magnetic field BB at an angle θ\theta is given by:

    F=qvBsin⁡θF = qvB\sin\theta
  3. Substitute the values into the formula.

    Substitute the given values into the formula:

    F=(3×10−6 C)×(2×105 m/s)×(0.5 T)×sin⁡(90∘)F = (3 \times 10^{-6} \text{ C}) \times (2 \times 10^5 \text{ m/s}) \times (0.5 \text{ T}) \times \sin(90^\circ)
  4. Calculate the magnetic force.

    Since sin⁡(90∘)=1\sin(90^\circ) = 1:

    F=(3×10−6)×(2×105)×(0.5)×1F = (3 \times 10^{-6}) \times (2 \times 10^5) \times (0.5) \times 1 F=(3×2×0.5)×(10−6×105)F = (3 \times 2 \times 0.5) \times (10^{-6} \times 10^5) F=(6×0.5)×(10−6+5)F = (6 \times 0.5) \times (10^{-6+5}) F=3×10−1F = 3 \times 10^{-1} F=0.3 NF = 0.3 \text{ N}

    The magnetic force acting on the charge is 0.3 N\text{0.3 N}.

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