An electron is moving in air at right angles to uniform magnetic field. The diagram below shows the path of the electron. The electron is slowing down.

Which one of the following correctly gives the direction of motion of the electron and the direction of the magnetic field ?

Rank the value of $\oint \overrightarrow{\mathbf{B}}·\mathrm{d}\overrightarrow{l}$ for the closed paths shown in figure from the smallest to largest:

Electrons moving with different speeds enter in uniform magnetic field in a direction perpendicular to the field. They will move along circular paths:

Electrons moving with different speeds enter in uniform magnetic field in a direction perpendicular to the field. If they move along circular paths, then the time periods of rotation will be:

Consider the three closed loops drawn using solid line in the magnetic field (magnetic field lines are drawn using dotted line) of an infinite curent-carrying wire normal to the plane of paper as shown.

Rank the line integral of the magnetic field along each path in order of increasing magnitude:

Only the current inside the Amperian loop contributes in:

An electron and a proton are moving under the influence of mutual forces. In calculating the change in the kinetic energy of the system during motion, one ignores the magnetic force of one on another. This is because:

Two charged particles traverse identical helical paths in a completely opposite sense in a uniform magnetic field B = ${\mathrm{B}}_0\hat{\mathrm{k}}$.

Biot-Savart law indicates that the moving electrons (velocity v) produce a magnetic field B such that:

In a cyclotron, a charged particle:

A circular current loop of magnetic moment M is in an arbitrary
orientation in an external magnetic field B. The work is done to rotate
the loop by 30° about an axis perpendicular to its plane is:

Consider a wire carrying a steady current, I placed in a uniform magnetic field B perpendicular to its length. Consider the charges inside the wire. It is known that magnetic forces do no work. This implies that,

(a) the motion of charges inside the conductor is unaffected by B since they do not absorb energy.
(b) some charges inside the wire move to the surface as a result of B.
(c) if the wire moves under the influence of B, no work is done by the force.
(d) if the wire moves under the influence of B, no work is done by the magnetic force on the ions assumed fixed within the wire.

Two identical current-carrying coaxial loops, carry current I in an opposite sense. A simple amperian loop passes through both of them once. Calling the loop as C,
a. $\oint \mathrm{B}.\mathrm{dl}=\mp 2{\mathrm{\mu }}_0\mathrm{I}$.
b. the value of $\oint \mathrm{B}.\mathrm{dl}$ is independent of the sense of C.
c. there may be a point on C where B and dl are perpendicular.
d. B vanishes everywhere on C.

A cubical region of space is filled with some uniform electric and magnetic fields. An electron enters the cube across one of its faces with velocity v and a positron enters via the opposite face with velocity - v. At this instant,

(a) the electric forces on both the particles cause identical accelerations.
(b) the magnetic forces on both the particles cause equal accelerations.
(c) both particles gain or lose energy at the same rate.
(d) the motion of the centre of mass (CM) is determined by B alone.

A charged particle would continue to move with a constant velocity in a region wherein,

(a) E = 0, B ≠ 0.
(b) E ≠ 0, B ≠ 0.
(c) E ≠ 0, B = 0.
(d) E = 0, B = 0.

A wire of length L meter carrying a current of I ampere is bent in the form of a circle. Its magnetic moment is, 

A straight wire of mass 200 g and length 1.5 m carries a current of 2 A. It is suspended in mid-air by a uniform horizontal magnetic field B (shown in the figure). What is the magnitude of the magnetic field?

The radius of the path of an electron and frequency (mass $9\times {10}^{-31} \mathrm{kg}$ and charge $1.6\times {10}^{-19} \mathrm{C}$) moving at a speed of 3 ×10⁷ m/s in a magnetic field of 6 × 10^–4 T perpendicular to it are respectively:

An electron $\left(mass 9\times {10}^{-31} kg and charge 1.6\times {10}^{-19} C\right)$ is moving at a speed of 3 ×10⁷ m/s in a magnetic field perpendicular to it. The energy of the electron in keV is: ( 1 eV = 1.6 × 10^–19 J)

A cyclotron’s oscillator frequency is 10 MHz. The radius of its ‘dees’ is 60 cm, what should be the operating magnetic field for accelerating protons and the kinetic energy (in MeV) of the proton beam produced by the accelerator?

An element $∆l=∆x\hat{i}$ is placed at the origin and carries a large current I =10 A (as shown in the figure). What is the magnetic field on the y-axis at a distance of 0.5 m? (∆x = 1 cm).

$$\begin{gathered} 1. 6\times {10}^{-8} T \\ 2. 4\times {10}^{-8} T \\ 3. 5\times {10}^{-8} T \\ 4. 5.4\times {10}^{-8} T \end{gathered}$$

A straight wire carrying a current of 12 A is bent into a semi-circular arc of radius 2.0 cm as shown in the figure. Consider the magnetic field B at the centre of the arc. What is the magnetic field due to the straight segments?

$$\begin{gathered} 1. 0 \\ 2. 1.2\times {10}^{-4} T \\ 3. 2.1\times {10}^{-4} T \\ 4. None of these \end{gathered}$$

Consider a tightly wound 100 turn coil of radius 10 cm, carrying a current of 1 A. What is the magnitude of the magnetic field at the centre of the coil?

$$\begin{gathered} 1. 8.2\times {10}^{-4} T \\ 2. 4.6\times {10}^{-4} T \\ 3. 5.2\times {10}^{-4} T \\ 4. 6.2\times {10}^{-4} T \end{gathered}$$

The figure shows a long straight wire of a circular cross-section (radius a) carrying steady current I. The current I is uniformly distributed across this cross-section. If the magnetic field in the region (r < a) is $B_1$ and for (r > a) is $B_2$, then $\frac{B_1}{B_2}$ is:

$$\begin{gathered} 1. \frac{a}{r} \\ 2. \frac{a^2}{r^2} \\ 3. \frac{r^2}{a^2} \\ 4. \frac{r}{a} \end{gathered}$$

A solenoid of length 0.5 m has a radius of 1 cm and is made up of 500 turns. It carries a current of 5 A. What is the magnitude of the magnetic field inside the solenoid?

$$\begin{gathered} 1. 6.28\times {10}^{-3} T \\ 2. 3.14\times {10}^{-3} T \\ 3. 2.72\times {10}^{-3} T \\ 4. 5.17\times {10}^{-3} T \end{gathered}$$

The horizontal component of the earth’s magnetic field at a certain place is 3.0 ×10^–5 T and the direction of the field is from the geographic south to the geographic north. A very long straight conductor is carrying a steady current of 1 A. What is the force per unit length on it when it is placed on a horizontal table and the direction of the current east to west?

$$\begin{gathered} 1. 3\times {10}^{-5} N m^{-1} \\ 2. 2\times {10}^{-7} N m^{-1} \\ 3. 0 \\ 4. 5\times {10}^{-7} N m^{-1} \end{gathered}$$

A 100 turn closely wound circular coil of radius 10 cm carries a current of 3.2 A. The magnetic field at the centre of the coil is:

$$\begin{gathered} 1. 4\times {10}^{-3} T \\ 2. 6\times {10}^{-3} T \\ 3. 2\times {10}^{-3} T \\ 4. 5\times {10}^{-3} T \end{gathered}$$