Magnetic Fields & Electromagnetism

According to the Biot-Savart Law, what happens to the magnetic field ($dB$) if the current ($I$) in the wire increases?

A short wire segment of length 2 mm carries a current of 5 A. At a point 3 cm away, the magnetic field due to this segment is measured. If $|d\vec{\ell} \times \hat{r}| = d\ell$, what is the magnitude of the magnetic field ($dB$)?

Consider two current segments $d\vec{l_1}$ and $d\vec{l_2}$ each carrying current $I$. They are positioned such that the magnetic field at point P due to $d\vec{l_1}$ is $\vec{B_1}$ and due to $d\vec{l_2}$ is $\vec{B_2}$. If $\vec{B_1}$ = (2,0,0) $\mu T$ and $\vec{B_2}$ = (0,3,0) $\mu T$, what is the net magnetic field at point P?

A circular loop carries a current in a counter-clockwise direction. What is the direction of the magnetic field at the center of the loop?

A circular loop with a radius of 5 cm carries a current of 2 A. What is the magnitude of the magnetic field at the center of the loop?

Two concentric circular loops have radii $R_1$ and $R_2$ ($R_1 < R_2$) and carry currents $I_1$ and $I_2$ respectively in the same direction. If the net magnetic field at the center is zero, what is the ratio of $I_1$ to $I_2$?

A straight wire carries a current in the upward direction. According to the right-hand rule, what is the direction of the magnetic field around the wire?

A wire carrying current $I$ is placed perpendicular to the page. At point P located to the right of the wire, the magnetic field is directed:

Two long, straight, parallel wires carry currents $I_1$ and $I_2$ in opposite directions. The current $I_1$ is 2A and $I_2$ is 4A. The distance between the wires is $d$. At what distance from the wire carrying $I_1$ is the magnetic field zero?

Under what condition is the force on a current-carrying wire in a magnetic field maximum?