Homemade ammeter (corrected)

Electricity and Magnetism Level 3

A conductor swing inside a magnetic flux density B = 0.5 T B = 0.5 \,\text{T} is deflected by an angle of α = 1 0 ∘ \alpha = 10^\circ due to the Lorentz force.

How large is the DC current I I through the conductor in units of milliamps (mA), to the nearest integer?


Details and Assumptions:

  • The conductor swing is a pendulum with mass m = 4 g m = 4\text{ g} .
  • Take the gravity acceleration as g = 10 m / s 2 g = 10 \,\text{m}/\text{s}^2 .
  • The lenght of the swinging conductor inside the magnetic field is l = 6 cm l = 6\, \text{cm} .


The answer is 235.

Markus Michelmann by Markus Michelmann , 35, Germany

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1 solution

Markus Michelmann
Sep 17, 2017

The electric current results from a charge density ρ = Q / V \rho = Q/V flowing with an average drift velocity v v through a cross sectional area A A . Therefore, I = j A = ρ v A = Q A l v A = Q v l I = j A = \rho v A = \frac{Q}{A l} v A = \frac{Q v}{l} with a volume V = A l V = A l for the conductor. The Lorenz force results F L = Q v B = I l B F_L = Q v B = I l B The balance of forces requires tan ⁡ α = F L F g \tan \alpha = \frac{F_L}{F_g} with the gravitional force F g = m g F_g = m g . Therefore, I = m g l B tan ⁡ α ≈ 235 mA I = \frac{m g}{l B} \tan \alpha \approx 235 \,\text{mA}

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