Infinite Current Sheet Magnetic Field Direction
The problem asks for the direction of the magnetic field ($\vec{B}$) produced by an infinite sheet with a uniform surface current density ($\vec{K}$) flowing in the positive $y$-direction ($\hat{j}$) over the $x$-$y$ plane.
Applying the Right-Hand Rule
We can determine the direction of the magnetic field using the right-hand rule, which relates the direction of current flow to the direction of the magnetic field it produces.
- Current Direction: The surface current flows uniformly in the positive $y$-direction ($\hat{j}$) across the infinite sheet lying in the $x$-$y$ plane ($z=0$).
- Right-Hand Rule Application:
- Imagine placing the thumb of your right hand in the direction of the current flow (positive $y$-direction).
- Curl your fingers around the current flow. The direction your fingers point represents the magnetic field lines.
- For an infinite sheet current, the magnetic field lines circle the current.
- Field Direction Above ($z > 0$): When you are above the sheet ($z > 0$), extending from the $x$-$y$ plane upwards, your curled fingers point in the positive $x$-direction ($\hat{i}$).
- Field Direction Below ($z < 0$): When you are below the sheet ($z < 0$), extending from the $x$-$y$ plane downwards, your curled fingers point in the negative $x$-direction ($-\hat{i}$).
Therefore, the magnetic field is directed along $\hat{i}$ for $z > 0$ and along $-\hat{i}$ for $z < 0$. This corresponds to Option A.
Important Questions from Magnetostatics Ampere's Law Vector Potential
- Consider a particle of mass $m = 9.0 \times 10^{-5} \text{ kg}$ and charge $q = 3.0 \times 10^{-4} \text{ C}$ in a uniform electromagnetic field $\vec{E} = 2\hat{x} \text{ V.m}^{-1}$, $\vec{B} = 3\hat{z} \text{ V.m}^{-2}\text{.s}$. The particle is released from the coordinates $(0, 5\text{ m}, 0)$ at time $t = 0$. Starting from initial speed zero, it comes back to the $y$-axis for the first time at time $t$. The value of $t$ in seconds (rounded off to two decimal places) is _____
The wire loop shown in the figure carries a steady current $I$. Each straight section of the loop has length $d$. A part of the loop lies in xy plane and the other part is tilted at $30^\circ$ with respect to the xz plane. The magnitude of the magnetic dipole moment of the loop (in appropriate units) is
- A linear magnetic material in the form of a cylinder of radius $R$ and length $L$ is placed with its axis parallel to the $z$ axis. The cylinder has uniform magnetization $\vec{M} \hat{k}$. Which of the following option(s) is/are correct?
- Consider an isolated magnetized sphere of radius $R$ with a uniform magnetization $\vec{M}$ along the positive $z$ direction, with the north and south poles of the sphere lying on the $z$ axis. It is given that the magnetic field inside the sphere is $\vec{B} = \frac{2\mu_0}{3} \vec{M}$, where $\mu_0$ is the permeability of vacuum. Which of the following statements is(are) CORRECT?
An infinitely long cylinder of radius $R$ carries a frozen-in magnetization $\vec M = ke^{-s^2} \hat z$, where $k$ is a constant and $s$ is the distance from the axis of cylinder. The magnetic permeability of free space is $\mu_o$. There is no free current present anywhere. The magnetic flux density ($\vec B$) inside the cylinder is
