Question

Faraday's Law of Induction states that a) a potential difference is induced in a loop when there is a change in the magnetic flux through the loop. b) the current induced in a loop by a changing magnetic field produces a magnetic field that opposes this change in magnetic field. c) a changing magnetic field induces an electric field. d) the inductance of a device is a measure of its opposition to changes in current flowing through it. e) magnetic flux is the product of the average magnetic field and the area perpendicular to it that it penetrates.

Short answer

Question: Based on Faraday's Law of Induction and related concepts, determine whether the following statements are true or false: a) Potential difference is induced in a loop. b) An opposing magnetic field is created in response to a changing magnetic field. c) A changing magnetic field induces an electric field. d) Inductance is a measure of opposition to changes in current. e) Magnetic flux can be calculated using the formula Φ = BA * cos(θ). Answer: a) True b) True c) True d) True e) True

Step-by-step solution

a) Potential difference induced in a loop

This statement is true. Faraday's Law of Induction states that the electromotive force (potential difference) induced in a loop is proportional to the rate of change of magnetic flux passing through the loop. Mathematically, this can be written as: EMF= -\frac{d\Phi}{dt} where EMF is the electromotive force, d\Phi is the change in magnetic flux, and dt is the change in time.

b) Opposing magnetic field

This statement is also true. This phenomenon is known as Lenz's Law, which is a consequence of Faraday's Law of Induction. Lenz's Law states that the direction of the induced current and its associated magnetic field will always be such that it opposes the change in the original magnetic field causing it.

c) Inducing an electric field

This statement is true. A changing magnetic field induces an electric field, as described by Faraday's Law of Induction. The induced electric field is what drives the electrons to move in a coil or conductor, thereby creating an induced current.

d) Inductance as a measure of opposition

This statement is true. Inductance (usually denoted by "L") is a measure of a device's (such as a coil or inductor) opposition to changes in current flowing through it. Mathematically, this can be expressed as: V = L \frac{di}{dt} where V is the potential difference across the device, L is the inductance, di is the change in current, and dt is the change in time.

e) Magnetic flux formula

This statement is true. Magnetic flux (denoted by "\Phi") is defined as the product of the average magnetic field (B) and the area (A) perpendicular to it that it penetrates. Mathematically, this can be expressed as: \Phi = BA \cdot \cos{\theta} where \theta is the angle between the magnetic field and the vector pointing perpendicular to the area.