Question

The loop in FIGURE EX30.13 is being pushed into the magnetic field at . The resistance of the loop is$0.10\mathrm{\Omega }$. What are the direction and the magnitude of the current in the loop?

Short answer

The magnitude of the current in the loop$I=5\mathrm{A}$with a clockwise direction

Step-by-step solution

Step1:Definition of magnitude

What is magnitude in Physics is undoubtedly a crucial question in science. Magnitude is a general term that refers to a quantity or a distance. In terms of motion, we can correlate magnitude with the size and speed of the object as it travels. The magnitude of an object or amount is its size.

Step2:Determine the charge through the wire

We want to find out how much electricity is flowing through the wire. We use Ohm's law to determine the current I flowing through the wire, as shown in the following equation.

$I=\frac{\epsilon }{R}$

Where R is the resistance of the wire. The wire is perpendicular to the magnetic field. Due to the motion of the wire, we can restate Faraday's law to get the magnitude of the emf in terms of the moving of wire using equation (30.3) in the form

$\epsilon =Blv$

Now, we plug the values for B, l, v and R into equation (3) to get I by

$I=\frac{Blv}{R}=\frac{\left(0.2\mathrm{T}\right)\left(0.05\mathrm{m}\right)(50\mathrm{m}/\mathrm{s})}{0.1\mathrm{\Omega }}$

Step3:Find the direction of current

According to Lenz's law, the direction of the induced emf drives current around a wire loop in such a way that it always opposes the change in magnetic flux that causes the emf. The magnetic field B inside the loop increases as the loop moves upward, so the induced magnetic field magnetic field opposite direction of the applied magnetic field B$(into the page), so the induced magnetic field magnetic field, a current is induced in the loop and we find that the current has a clockwise direction by applying the right-hand rule