Why is the magnetic field strength greater inside a current carrying loop of wire than about a straight section of wire?

Is the rule for the interaction between magnetic poles similar to the rule for the interaction between electrically charged particles?

A small bar magnet experiences a 0.020 N m torque when the axis of the magnet is at $45^{\circ}$ to a 0.10 T magnetic field. What is the magnitude of its magnetic dipole moment?

A square loop of wire, of side $d$, carries a current $I$. Show that the magnetic field at the center of the square is

A square current loop 5.0 cm on each side carries a 500 mA current. The loop is in a 1.2 T uniform magnetic field. The axis of the loop, perpendicular to the plane of the loop, is $30^{\circ}$ away from the field direction. What is the magnitude of the torque on the current loop?

Three long wires all lie in an $x y$ plane parallel to the $x$ axis. They are spaced equally, $10 \mathrm{~cm}$ apart. The two outer wires each carry a current of $5.0 \mathrm{~A}$ in the positive $x$ direction. What is the magnitude of the force on a $3.0 \mathrm{~m}$ section of either of the outer wires if the current in the center wire is $3.2 \mathrm{~A}$ in the negative $x$ direction?

Three long wires all lie in an xy plane parallel to the x axis. They are spaced equally, 10 cm apart. The two outer wires each carry a current of 5.0 A in the positive x direction. What is the magnitude of the force on a 3.0 m section of either of the outer wires if the current in the center wire is 3.2 A in the positive x direction?

Three long wires all lie in an xy plane parallel to the x axis. They are spaced equally, 10 cm apart. The two outer wires each carry a current of 5.0 A in the positive x direction. What is the magnitude of the force on a 3.0 m section of either of the outer wires if the current in the center wire is 3.2 A in the negative x direction?

What is the force (including direction) per unit length on wire 1 in figure (parallel current carrying wires) ?

Three long, straight wires are carrying currents that have the same magnitude. In C the current is opposite to the current in A and B. The wires are equally spaced. Each wire experiences a net force due to the other two wires. Which wire experiences a net force with the greatest magnitude? (a) A (b) B (c) C (d) All three wires experience a net force that has the same magnitude.

Determine the magnitude and direction of the force between two parallel wires 35 m long and 6.0 cm apart, each carrying 25 A in the same direction.

A bar magnet is initially far from a circular loop of wire. The magnet is moved at constant speed along the axis of the loop. It moves toward the loop, proceeds to pass through it, and then continues until it is far away on the right side of the loop. Sketch a qualitative graph of the current in the loop as a function of the position of the bar magnet. Take the current to be positive when it is counterclockwise.

Find the tangential and normal components of the acceleration vector. r(t) = 6(3t − t3) i + 18t2 j.

Use a calculator to evaluate the line integral correct to four decimal places. $\int_{C} \mathbf{F} \cdot d \mathbf{r},$ where $\mathbf{F}(x, y, z)=y z e^{x} \mathbf{i}+z x e^{y} \mathbf{j}+x y e^{z} \mathbf{k}$ and $\mathbf{r}(t)=\sin t \mathbf{i}+\cos t \mathbf{j}+\tan t \mathbf{k}, 0 \leqslant t \leqslant \pi / 4$