Magnetic Effects of Current and Magnetism

According to Ampere’s Circuital Law, the line integral of the magnetic field $\oint \vec{B} \cdot d\vec{l} = \mu_0 \sum I$, where $\sum I$ is the algebraic sum of currents enclosed by the Amperian loop. In the provided diagram, $I_1$ (acting outwards) and $I_2$ (acting inwards) are enclosed by the loop, while $I_3$ is outside. What is the net current $\sum I$ for this loop?

For a long straight wire, the graph of magnetic field $B$ versus the distance $r$ from the axis (for $r >$ radius of wire) is a:

The total number of turns in a toroid is $N$. If the average radius is $R$, the turns per unit length $n$ is calculated as:

The magnetic field inside a long straight solenoid is non-zero, while the field outside an ideal solenoid is assumed to be:

According to Ampere's law, if the magnetic field is zero everywhere on a closed path, it implies that:

The dimension of the quantity $B^2 / (2 \mu_0)$ (magnetic energy density) is the same as that of:

A current element $I d\vec{l}$ is placed at $(a, 0, 0)$ and carries current in the $+y$ direction. The magnetic field at the origin is:

If the current in a circular coil is doubled and the radius is halved, the magnetic field at the center becomes:

A square loop of side $a$ carries current $I$. It is placed in a uniform magnetic field $B$ such that the plane of the loop is at $30^{\circ}$ to the field. The torque on the loop is:

A circular loop of radius $R$ carries a current $I$. At what distance $x$ from the center along the axis is the magnetic field $1/8$th of its value at the center?

Which of the following is correct regarding a galvanometer converted to an ammeter?

If the plane of a current loop is perpendicular to the magnetic field, the torque on it is:

The pointer of a moving coil galvanometer stops at a particular position when:

To convert a $100 \Omega$ galvanometer into a voltmeter of range $0 - 10 V$, if the full-scale current is $1 mA$, the series resistance required is:

Two identical galvanometers are converted, one into an ammeter and another into a milliammeter. Which one will have a higher resistance?

Why is the soft iron core used in a moving coil galvanometer?

If the current sensitivity of a galvanometer is increased by $50\%$, but the resistance is also doubled, what is the new voltage sensitivity compared to the original $V_s$?

A galvanometer has a resistance of $15 \Omega$ and gives full-scale deflection for $2 \text{ mA}$. How many $985 \Omega$ resistors in series are needed to convert it into a $100 \text{ V}$ voltmeter?

A square loop of side $a$ and a circular loop of radius $r$ carry the same current and have the same magnetic moment. What is the ratio $a/r$?

To convert a galvanometer into an ammeter, a shunt $S$ is used. If we want to double the range of this ammeter, the new shunt $S'$ should be:

If $B_H = \sqrt{3} B_V$ at a specific place, what is the value of the angle of dip?

When a magnetic needle is free to rotate in a horizontal plane, it comes to rest along the:

If the Earth is imagined as a giant bar magnet, its North pole is located in the southern hemisphere near the:

At a place where the dip angle is $\delta$, the total field intensity $B$ is related to $B_H$ as:

The magnetic field intensity of the Earth at the surface is of the order of:

A place where the magnetic needle stands vertical has an angle of dip equal to:

What is the angle of dip at a place where the Earth's magnetic field is entirely horizontal?

A deflection magnetometer is adjusted in the Tan A position. When a magnet is placed at a distance $r$ from the needle, the deflection is $60^{\circ}$. If the distance is doubled, the deflection will be:

A bar magnet of moment of inertia $I$ and magnetic moment $M$ is vibrating in a magnetic field $B$. If the magnetic moment is doubled and the moment of inertia is halved, the new frequency of vibration is:

What is the angle of dip at a place where the ratio of the vertical component to the total magnetic field is $1/2$?

The susceptibility $(\chi)$ of a paramagnetic substance is:

The magnetism of a magnet can be destroyed by:

Which of the following types of materials does NOT have permanent magnetic dipoles?

Water is a:

Which physical quantity is represented by the slope of the $B$ vs $H$ curve for a linear magnetic material in the initial stage?

The susceptibility of a paramagnetic material at $27^{\circ}\text{C}$ is $0.0030$. What is its susceptibility at $127^{\circ}\text{C}$?

Gadolinium is a material that is ferromagnetic below $19^{\circ}\text{C}$. Above this temperature, it behaves as a:

The susceptibility of a paramagnetic material is $\chi$ at $27^\circ\text{C}$. What is the susceptibility at $-73^\circ\text{C}$?

If the susceptibility of a material is very large ($> 1000$), the relation $B = \mu_0 (H + M)$ can be approximated as:

What is the primary reason for the energy loss in the form of heat in a transformer core?