Moving Charges and Magnetism

The direction of $d\vec{l}$ in the Biot-Savart Law is always:

Which constant is found in the Biot-Savart Law but not in Coulomb's Law?

The magnetic field $B$ at the center of a loop is $B_0$. If the radius of the loop is tripled while the current remains the same, the new field will be:

If the angle between the current element and the position vector increases from $30^\circ$ to $90^\circ$, the magnetic field magnitude:

Two wires $A$ and $B$ carry the same current $I$. Wire $A$ is a straight wire of infinite length and wire $B$ is a circular loop of radius $R$. The ratio of magnetic field at distance $R$ from wire $A$ to the magnetic field at the center of loop $B$ is:

If the number of turns in a circular coil is doubled and its radius is also doubled, the magnetic field at its center for the same current will:

A circular loop of radius $R$ carries current $I$. The magnetic field at the center is $B$. At what distance $x$ on the axis is the field $B/8$?

Two identical wires are bent into a semi-circle of radius $R$ and a square of side $a$ respectively. If they carry the same current and the magnetic fields at their centers are equal, the ratio $R/a$ is:

In a hydrogen atom, an electron revolves around a proton in an orbit of radius $0.53 \text{ \AA}$ with a speed of $2.2 \times 10^6 \text{ m/s}$. The magnetic field at the center of the orbit is approximately:

A current $I$ flows in a circular loop of radius $R$. The magnetic field at a point on the axis at distance $x$ is $B$. If $x >> R$, $B$ varies as:

Which of the following mathematical expressions correctly represents Ampere’s Circuital Law for a closed loop enclosing a steady current $I$?

The SI unit of magnetic permeability $\mu_0$ is:

If the current in a long straight conductor is doubled, how does the magnetic field at a distance $r$ change?

What is the magnetic field at the center of a toroid of mean radius $r$ having $N$ total turns and carrying current $I$?

Consider a thick long wire of radius $R$ carrying a steady current $I$ uniformly distributed across its cross-section. According to Ampere's law, how does the magnetic field $B$ vary with distance $r$ from the axis for the region $r < R$?

A long straight solenoid has $n$ turns per unit length and carries a current $I$. What is the magnetic field $B$ inside the solenoid at a point far from the ends, as derived using Ampere's Law in the path shown?

In a coaxial cable, the central conductor carries current $I$ and the outer shield carries the return current $I$ in the opposite direction. The magnetic field at a point outside the cable is:

A cylindrical conductor of radius $R$ carries a current $I$. However, the current is not uniform; the current density varies as $J = J_0(1 - r^2/R^2)$. Using Ampere's law, find the ratio of the magnetic field at $r = R/2$ to the magnetic field at the surface $r = R$.

Two long parallel wires are separated by a distance $D = 20\text{ cm}$. Wire 1 carries $10\text{ A}$ into the page and Wire 2 carries $20\text{ A}$ out of the page. Find the distance from Wire 1 along the line connecting them (between the wires) where the magnetic field is exactly $4 \times 10^{-5}\text{ T}$.

A physicist constructs a non-ideal solenoid where the winding density $n$ varies with the radial distance $r$ as $n(r) = n_0(1 - r/a)$, where $a$ is the solenoid radius. If a current $I$ flows through the windings, find the expression for the magnetic field $B$ at the center (axial) using the approximation of an infinite solenoid.

If a charge $q$ moves with velocity $v$ at an angle of $90^\circ$ to a field $B$, the magnetic force is:

Which of the following is not a property of the magnetic force on a moving charge?

A charged particle is projected into a magnetic field. The force is zero if the particle is projected at an angle of:

One Tesla is equivalent to:

A charge $q$ is moving along a circle of radius $r$ with velocity $v$ in a uniform magnetic field $B$. The magnitude of the magnetic force is $F$. If $v$ is halved and $B$ is doubled, the force becomes:

A particle moves in a region where both $\vec{E}$ and $\vec{B}$ are non-zero. If the velocity $\vec{v}$ is parallel to $\vec{E}$ and $\vec{E}$ is perpendicular to $\vec{B}$, the magnetic force on the particle is:

If an electron and a proton enter a magnetic field with the same velocity perpendicular to the field, the electron will:

Two particles with the same momentum enter a magnetic field $B$ at $30^\circ$ and $60^\circ$ respectively. What is the ratio of the radii of their helical paths if they have the same charge and mass?

A charge $q$ is moving in a region of uniform magnetic field $B$. The time period of its circular motion is $T$. If the mass of the particle is doubled and the charge is halved, what will be the new time period?

A particle of mass $m$ and charge $q$ is moving in a magnetic field $\vec{B} = B_0(\hat{i} + \hat{j})$. If the velocity at $t=0$ is $\vec{v} = v_0\hat{k}$, the path of the particle is a:

The deflection produced in a galvanometer when a unit voltage is applied across its terminals is called:

The ratio of current sensitivity to voltage sensitivity is equal to:

In the formula $\tau = NIAB \sin \theta$, the radial field in an MCG ensures that $\theta$ for the area vector and $B$ is:

For a galvanometer with figure of merit $k'$, the current $I$ for a deflection of $\theta$ divisions is:

In a galvanometer, the sensitivity can be increased by using a suspension wire of material having:

If a galvanometer resistance is $G$, and it is shunted by $G$, the range of the ammeter becomes how many times the original $I_g$?

A voltmeter of range $10 \, V$ has a resistance of $10,000 \, \Omega$. To double its range, what resistance should be connected in series with it?

To increase the voltage sensitivity of an MCG by $50\%$, one could:

A galvanometer with resistance $10 \, \Omega$ is connected to a $2 \, V$ battery in series with a $1990 \, \Omega$ resistor. If it shows a deflection of $20$ divisions, the figure of merit is:

A moving coil galvanometer has a dead-beat response. This means:

In a cyclotron, the particles are accelerated by the:

The pitch of a helical path is the distance traveled by the particle along the magnetic field in:

Which of the following does not experience a force when placed in a magnetic field?

The sensitivity of a galvanometer is defined as:

A charged particle of mass $m$ and charge $q$ is projected into a uniform magnetic field $B$ at an angle $\theta$ $(0 < \theta < 90^\circ)$ with the field lines. If $r$ represents the radius of the circular part of its motion and $p$ represents the pitch of its helical path, the ratio $\frac{r}{p}$ is given by:

A charged particle is moving in a circle of radius $R$ in a magnetic field. If the kinetic energy is quadrupled, the new radius is:

An alpha particle and a proton are moving in the same magnetic field with the same speed. The ratio of the period of the alpha particle to that of the proton is:

What is the work done by a magnetic field on a particle of charge $q$ moving in a circle of radius $r$?

Two charges $q$ and $-q$ are moving with the same velocity $v$ entering a magnetic field $B$ perpendicularly. They will describe circular paths of:

A current $I$ flows through a circular loop of radius $R$. The magnetic field at the center is $B$. If the radius is doubled and current is halved, the magnetic field at the center becomes:

Dimensions of magnetic field $B$ are:

What is the magnetic field at the center of a circular arc of radius $R$ subtending an angle $\theta$ at the center?

The magnetic field on the axis of a circular loop is always ________ to the plane of the loop.

If a circular loop of radius $1$ m carries a current of $1$ A, the magnetic field at its center is:

Two circular loops $A$ and $B$ have radii $R$ and $2R$ and carry currents $I$ and $2I$ respectively. The ratio of the magnetic fields at their centers is:

The magnetic field $B$ at the center of a circular current loop of radius $R$ is $100 \mu T$. What is the field at a distance $x = R\sqrt{3}$ on its axis?

A circular coil of radius $R$ has $n$ turns. The magnetic field at a distance $x$ on the axis is $B$. If the number of turns is doubled and the radius is halved (same current), the new field at the center is:

A circular coil of radius $R$ and $N$ turns carries current $I$. The magnetic field at a distance $x$ on the axis is $B$. If the number of turns is doubled, the radius is halved, and the current is halved, the magnetic field at the center will be:

For a circular loop of radius $R$, the magnetic field at an axial distance $x$ is $B$. If $x \gg R$, the field $B$ varies as:

Two identical coaxial coils carry current $I$ in opposite directions. The magnetic field at a point on the axis exactly halfway between them is zero. The gradient of the magnetic field ($dB/dx$) at this point is:

To get a uniform magnetic field in a large volume, we generally use a:

The magnetic field lines of a solenoid enter the solenoid at the:

What is the value of the magnetic field at a point on the axis of a solenoid but far away from it?

A student winds a wire closely on a glass tube. This device is most likely a:

A solenoid has $n$ turns per unit length. If the same wire is used to make another solenoid with $n/2$ turns per unit length, keeping the total length same, the resistance of the new solenoid will be:

The field inside a solenoid is $B$. If a paramagnetic material of susceptibility $\chi$ is placed inside, the new field will be:

A solenoid of length $1\text{ m}$ and diameter $3\text{ cm}$ has $500$ turns. For a current of $2\text{ A}$, the magnetic field at the center is $B$. If the diameter is increased to $6\text{ cm}$, the field at the center becomes:

A long solenoid has $n$ turns per unit length. The current $I$ varies with time as $I = kt$. The induced electric field $E$ at a distance $r < R$ from the axis is:

A solenoid of length $L$ and turns $N$ is connected to a battery. If the core is filled with a paramagnetic material, what happens to the force between the individual turns of the solenoid?

If a solenoid is placed in a region with an external uniform magnetic field $B_{ext}$ parallel to its axis, the total field inside is $B_{total} = \mu_0 n I + B_{ext}$. If the external field is reversed, the magnetic pressure on the solenoid walls will:

When current is passed through a solenoid, its coils:

Two parallel wires carrying equal currents in the same direction are placed 1 m apart. If the force per unit length is $2 \times 10^{-7} N/m$, the current in each wire is:

The force between two parallel wires is independent of the:

The magnetic force between parallel wires is proportional to the _____ of the currents.

Force between two parallel currents is an example of:

Which constant appears in the denominator of the force per unit length formula for parallel wires?

If the currents in two parallel wires are $I_1$ and $I_2$ in opposite directions, the force on a unit length of wire 2 due to wire 1 is directed:

Two parallel wires carry current $I$ and $I$ in same direction. If we double the currents and double the distance, the force per unit length:

What is the force between two parallel currents each of $1\, A$ and $1\, m$ long, if they are $1\, km$ apart?

Two parallel wires are carrying currents in the same direction. A proton is projected midway between the wires with a velocity $v$ perpendicular to the plane of the wires. Its path will be:

The expression for torque on a current loop is $\tau = NIAB \sin \theta$. Here $\theta$ is the angle between:

Current sensitivity of a galvanometer increases if:

If a magnet is broken into two pieces, the magnetic moment of each piece (compared to the original) will be:

The angle between $\vec{M}$ and $\vec{B}$ for which torque is half its maximum value is:

A loop of wire carries current $I$. If it is placed in a uniform magnetic field, the torque depends on its area $A$ as:

Two small identical magnets are placed perpendicularly to each other. If their magnetic moments are $M$ and $M$, the resultant magnetic moment is:

The magnitude of torque on a magnetic dipole depends on:

In a moving coil galvanometer, the magnetic field is made radial so that:

The magnetic moment of a Bohr magneton is approximately:

A uniform disc of mass $M$ and radius $R$ has a charge $Q$ distributed uniformly on its surface. It rotates with angular velocity $\omega$ about its central axis. The magnetic moment is: