# Faraday's Law Practice Problems

A square loop of side 25.0 cm is inserted into a magnetic field directed into the page. Initially, the magnetic field has a magnitude of 0.950 T. The rate of decrease of the magnetic field is -0.0650 T/s. Consider an insulator in the loop separating two ends of the loop from touching. Calculate the emf induced in between the ends.

The magnetic field is increasing at a rate of 0.0500 T/s through a circular solenoid of a radius of 10 cm. A square loop of length 30cm is centered about the axis of the solenoid. Determine the emf induced in the loop

The magnetic field is increasing at a rate of 0.0500 T/s through a circular solenoid of a radius of 10 cm. A circular loop of diameter 9.0 cm is centered about the solenoid axis. Calculate the emf induced in the loop

Consider a uniform magnetic field that is perpendicular to the plane of the area of a circular coil having a radius of 5 cm, moving with a speed of 5 m/s. Determine the induced emf in the coil if the speed and magnetic field are both doubled.

A circular coil with a radius of 1.80 cm and 150 turns rotates in a magnetic field of 0.0650 T. If 28.0 mV is the maximum emf produced, calculate the angular speed of the coil.

A circular conductor with a radius of 2.50 cm is placed in a uniform magnetic field of 1.23 T decreasing gradually at a rate of 0.450 T/s. Calculate the magnitude of the induced electric field in the conductor.

A circular loop is inserted into a magnetic field directed into the page. Initially, the magnetic field has a magnitude of 0.850 T. The rate of decrease of the magnetic field is -0.0400 T/s. Determine the shape of the field lines for the electric field induced.

During an experiment, a group of students are supplied with a solenoid of radius 1.30 cm and has 500 turns per meter. A magnetic field is directed through the solenoid inducing a uniformly increasing current. The magnitude of the electric field induced is 6.00 × 10^{-6} V/m measured around the midpoint of the solenoid and at a radial distance of 4.50 cm from the solenoid's axis. Determine the numerical value of the current change rate.

Current is increasing uniformly at a rate of 38.0 A/s through a solenoid with a radius of 3.0 cm and has 800 turns per meter. Calculate the electric field induced, measured near the midpoint of the solenoid at a radial distance of i) 0.75 cm and ii) 1.25 cm from the solenoid's axis.

A current of 0.450 A flows through a winding in the form of a linear solenoid having 80 turns of wire per cm and a cross-sectional area of 7.00 cm^{2}. It is bounded by a secondary winding of 15 turns. Turning off the current in the solenoid reduces the magnetic field of the solenoid to zero in 0.0700 s. Calculate the mean emf induced in the second winding.

A 100 turns circular coil has a radius of 30 cm. It is placed in a uniform 2.1 T magnetic field. The orientation of the coil's plane relative to the magnetic field is changed from 35 degrees to 85 degrees in 0.0800 s. Calculate the mean induced emf in the coil.

The figure given shows a conductor pq in contact with metal rails mp and nq with a uniform magnetic field of 0.650 T around it, perpendicular to the plane of the figure. Find the direction of current flow in the conductor.

In a Physics experiment, a spring is stretched into a square loop of perimeter 200 cm using four rods and is placed in a uniform magnetic field of 0.8T oriented parallel to the axis of the loop. Its perimeter varies with time, decreasing at a rate of 18.0 cm/s as the rods are moved closer to each other. The magnetic field is oriented parallel to the axis of the square loop. Determine the direction of the induced current relative to an observer viewing in the direction of the magnetic field.

A team of scientists designed and created a conducting polymer-based wire that is super stretchable and has high conductivity. The wire is stretched into a circular loop of circumference 2 m. The wire is placed with its plane perpendicular to a uniform 0.200 T magnetic field. When released, the circumference of the loop starts to shrink at a uniform rate of 15.0 cm/s. Determine the induced emf in the loop after exactly 11s.

A copper wire is wrapped around a rod of uniform thickness. The length of the wire has a resistance of 0.500 Ω and produces a coil that has only one complete turn of area 0.0400m^{2}. The turn is then placed in a uniform magnetic field oriented parallel to the axis of the loop and has a magnitude of 6.21 T. Determine the current induced in the loop if the magnetic field increases at a rate of 0.315 T/s.

Consider a rectangular coil. A varying magnetic field is applied to the coil and it passes through the single loop. The single loop has an area of 0.0700 m^{2}. The magnetic field is parallel to the coils axis and decreases at a rate of 0.250T/s. Find the emf induced if the magnetic field has an initial value of 2.70T.

A rectangular loop made of silver, 4.0 m by 1.5 m, with a mass of 10.0 kg and resistance of 0.016 Ω, is propelled at 4.0 m/s into a 0.25 T magnetic field starting at x=0 m. The field is perpendicular to the loop. From t=0 s, calculate and draw a graph of v over the interval 0 s≤t≤5.0 s as it moves along the x-axis, assuming no gravity or air resistance, and that the 1.5 m side of the loop is the first to enter the field.

Consider a solenoid with a length of 2.2 m and a diameter of 15 cm. It is wound with 2500 turns of a highly conductive wire (zero-resistance). At an equidistant point from the solenoid's axis and its windings, the induced electric field after 1.0 s is 6.8 × 10^{ −3} V/m. If it only takes 4.0 s for the current within the solenoid to soar from zero to its peak value when the magnet is activated, determine the solenoid's magnetic field when the current has stabilized.

Find the value of the current I, at t = 8.0 s, given a solenoid with 12 turns that has a resistive value of R = 0.8 Ω. The solenoid is positioned within a magnetic field that varies over time, given by B = 0.040t + 0.013 t ^{2} Teslas. This magnetic field is directed perpendicular to the plane of the solenoid. The radius of the solenoid is 3.0 cm.