Question

Large electric fields are certainly a hazard to the human body, as they can produce dangerous currents, but what about large magnetic fields? A man \(1.80 \mathrm{~m}\) tall walks at \(2.00 \mathrm{~m} / \mathrm{s}\) perpendicular to a horizontal magnetic field of \(5.0 \mathrm{~T} ;\) that is, he walks between the pole faces of a very big magnet. (Such a magnet can, for example, be found in the National Superconducting Cyclotron Laboratory at Michigan State University.) Given that his body is full of conducting fluids, estimate the potential difference induced between his head and feet.

Short answer

Answer: The potential difference induced between the man's head and feet is 18.0 V.

Step-by-step solution

Identify the given values

We are given the following values in the problem: - Height of the man (L): 1.80 m - Walking speed (v): 2.00 m/s - Magnetic field (B): 5.0 T

Apply the motional EMF formula

Using the given values, we can apply the motional EMF formula to find the potential difference induced in the man's body. As we mentioned earlier, the formula is: EMF = vBL Plugging in the given values, we get: EMF = (2.00 m/s)(5.0 T)(1.80 m)

Calculate the potential difference

Now, we will multiply the values together to find the potential difference: EMF = 18.0 V The potential difference induced between the man's head and feet is 18.0 V.

Key concepts

Magnetic Fields

Magnetic fields are fundamental forces of nature, often visualized as lines of force that exit a magnetic north pole and enter a magnetic south pole. These fields are created by moving charges, such as an electric current flowing through a wire, or by the intrinsic magnetic moments of elementary particles associated with a fundamental quantum property called spin.

Magnetic fields exert forces on other moving charges or magnetic materials within the field. This interaction is the basis for the operation of countless devices, from electric motors to MRI machines. In our exercise, a strong magnetic field of 5.0 Tesla, which is far greater than the Earth's natural magnetic field, interacts with the conducting elements inside the human body, leading to an induced potential difference.

Electromagnetic Induction

Electromagnetic induction is a process where a conductor moving through a magnetic field, or a changing magnetic field around a stationary conductor, induces an electromotive force (EMF), or voltage. This phenomenon was discovered by Michael Faraday and is harnessed in many electrical devices such as generators and transformers.

In the textbook exercise, as the man walks perpendicularly through a magnetic field, his body acts as a conductor and experiences this fundamental effect. The fluids in his body containing charged particles (ions) move through the magnetic field, which induces an EMF along the length of his body, creating a potential difference between his head and feet. This potential difference can be calculated using the formula EMF = vBL, where 'v' is the velocity of the conductor, 'B' is the magnetic field strength, and 'L' is the length of the conductor.

Electric Fields

Electric fields represent the force fields surrounding electric charges, and they exert forces on other charges within the field. The strength of the electric field at each point is defined as the force per unit charge that would be felt by a stationary test charge placed at that point. These fields are crucial to understanding the behavior of charges and the flow of current in conductive materials.

Although our exercise focuses primarily on the effects of a magnetic field, the concept of electric fields is inherently linked due to the induced EMF. The generated potential difference within the man's body implies the existence of an electric field directed along his body's length. If left unhindered, this electric field would cause current to flow within the body. Fortunately, the human body has high resistance which prevents dangerous currents from flowing in such situations.