Magnetic Field Of Current

1. Describe the magnetic field produced by a proton beam moving away from you (into the page).
2. Describe the magnetic field produced by an electron beam moving toward you (out of the page). Sketch both fields.

1. When the coil plane is perpendicular to the magnetic field direction, what is the magnetic flux through the coil?
2. When the coil is rotated by $60°$ about the $OO'$ axis from the position above, what is the magnetic flux through the coil?

1. Find the magnitude and direction of the magnetic flux density on the $y$-axis at $y = -3 \text{ cm}$.
2. Find the magnitude and direction of the magnetic flux density on the $y$-axis at $y = +3 \text{ cm}$.
3. Find the force per unit length that one wire exerts on the other.

Two infinite straight wires are perpendicular to each other but do not intersect; their minimum separation is $d = 2.0 \text{ cm}$. They carry currents $I_1 = 4.0$ A and $I_2 = 6.0$ A. Point $P$ in the field lies at perpendicular distance $d$ from each wire. Find the magnitude of the magnetic flux density $\vec{B}$ at $P$.

1. Radially away from the wire.
2. Parallel to the wire and in the same direction as the current.
3. Perpendicular to the wire and tangent to the circular field line at the electron's location.

A long straight wire carries a current $I_1 = 30$ A. In the same plane as this wire, a rectangular conducting loop of length $L = 30 \text{ cm}$ and width $w = 8 \text{ cm}$ carries current $I_2 = 20$ A. The long sides of the loop are parallel to the wire; the side of the loop nearest the wire is at distance $a = 1 \text{ cm}$ from it, and the current in this near side flows in the same direction as the current in the straight wire. Find the magnitude and direction of the net magnetic force that the straight wire exerts on the loop.

A solenoid is $L = 1.0 \text{ m}$ long with average diameter $D = 3.0 \text{ cm}$. It has $5$ layers of windings with $850$ turns per layer, and carries a current $I = 5.0 \text{ A}$. Find the magnetic flux density at the center of the solenoid.

A solenoid has length $L = 50 \text{ cm}$ and radius $r = 1 \text{ cm}$, with a total of $N = 400$ turns carrying a current $I = 3 \text{ A}$. Find the magnetic flux through the solenoid's central cross-section.