Electromagnetic Induction

A flat surface with area 2.0 \,\text{m}^2 is in a uniform magnetic field of 0.5 \,\text{T}. The magnetic field is oriented at an angle of 30^\circ with respect to the area vector. What is the magnetic flux through the surface?

A circular loop of radius $r = 0.1 ,\text{m}$ is placed in a uniform magnetic field of magnitude $B = 0.3 ,\text{T}$. The magnetic field is oriented perpendicular to the plane of the loop. What is the magnetic flux through the loop?

A magnetic field is given by $\vec{B} = (2x \hat{i}) ,\text{T}$, where $x$ is in meters. A square loop of side 0.5 \,\text{m} is placed in the yz-plane with one corner at the origin. What is the magnetic flux through the loop?

A square loop with side length $a$ is placed in a uniform magnetic field $B$. Initially, the loop is oriented such that the magnetic field is perpendicular to the area vector. The loop is then rotated until the magnetic field is parallel to the plane of the loop. What is the change in magnetic flux through the loop?

A conducting loop is placed in a region of increasing magnetic field pointing into the page. According to Lenz's Law, the direction of the induced current in the loop will be...

According to Faraday's Law, a changing magnetic flux through a loop of wire induces what?

What does magnetic flux quantify?

A non-uniform magnetic field is given by $\vec{B} = (x^2 \hat{i} + y^2 \hat{j}) ,\text{T}$. Calculate the magnetic flux through a square surface of side length $a$ lying in the xy-plane with vertices at $(0,0)$, $(a,0)$, $(a,a)$, and $(0,a)$.