Ampere's law gives a method to calculate the magnetic field due to given current distribution. According to it, the circulation \(\oint \vec{B} \cdot d \vec{l}\) of the resultant magnetic field along a closed plane curve is equal to \(\mu_{0}\) times the total current crossing the area bounded by the closed curve provided the electric field inside the loop remains constant. Ampere's law is more useful under certain symmetrical conditions. Consider one such case of a long Straight wire with circular cross-section (radius R) carrying current I uniformly distributed across this cross-section.

(i) The magnetic field at a radial distance r from the centre of the wire in the region r > R, is

(ii) The magnetic field at a distance r in the region r < R is

(iii) A long straight wire of a circular cross section (radius a) carries a steady current I and the current I is uniformly distributed across this cross-section. Which of the following plots represents the variation of magnitude of magnetic field B with distance r from the centre of the wire?

(iv) A long straight wire of radius R carries a steady current I. The current is uniformly distributed across its cross-section. The ratio of magnetic field at R/2 and 2R is

(v) A direct current I flows along the length of an infinitely long straight thin walled pipe, then the magnetic field is

An electron with speed V_o << c moves in a circle ofradius r_o in a uniform magnetic field. This electron is able to traverse a circular path as magnetic field is perpendicular to the velocity of the electron. A force acts on the particle perpendicular to both \(\vec{v}_{0}\) and \(\vec{B}\). This force continuously deflects the particle sideways without  changing its speed and the particle will move along a circle perpendicular to the field. The time required for one revolution of the electron is T_o .

(i) If the speed of the electron is now doubled to 2v_o.The radius of the circle will change to

(ii) If v_o = 2v_o then the time required for one revolution of the electron will change to

(iii) A charged particles is projected in a magnetic field \(\vec{B}=(2 \hat{i}+4 \hat{j}) \times 10^{2} \mathrm{~T}\) The acceleration of the particle is found to be \(\vec{a}=(x \hat{i}+2 \hat{j}) \mathrm{m} \mathrm{s}^{-2}\). Find the value of x.

(iv) If the given electron has a velocity not perpendicular to B, then trajectory of the electron is

(v) If this electron of charge (e) is moving parallel to uniform magnetic field with constant velocity v, the force acting on the electron is

A magnetic field can be produced by moving, charges or electric currents. The basic equation governing the magnetic field due to a current distribution is the Biot-Savart law.
Finding the magnetic field resulting from a current distribution involves the vector product, and is inherently a calculas problem when the distance from the current to the field point is continuously changing.
According to this law, the magnetic field at a point due to a current element oflength \(d \vec{l}\) carrying current I, at a distance r from the element is \(d B=\frac{\mu_{0}}{4 \pi} \frac{I(d \vec{l} \times \vec{r})}{r^{3}}\)
Biot -Savart law has certain similarities as well as difference with Coloumbs law for electrostatic field e.g., there is an angle dependence in Biot-Savart law which is not present in electrostatic case.
(i) The direction of magnetic field \(d \vec{B}\) due to a current element \(I d \vec{l}\) at a point of distance \(\vec{r}\) from it, when a current I passes through a long conductor is in the direction

(ii) The magnetic field due to a current in a straight wire segment of length L at a point on its perpendicular bisector at a distance r (r >> L)

(iii) Two long straight wires are set parallel to each other. Each carries a current i in the same direction and the separation between them is 2r. The intensity of the magnetic field midway t between them is

(iv) A long straight wire carries a current along the z-axis for any two points in the x - y plane. Which of the following is always false?

(v) Biot-Savart law can be expressed alternatively as

Moving coil galvanometer operates on Permanent Magnet Moving Coil (PMMC) mechanism and was designed by the scientist D'arsonval.
Moving coil galvanometers are of two types
(i) Suspended coil
(ii) Pivoted coil type or tangent galvanometer.
Its working is based on the fact that when a current carrying coil is placed in a magnetic field, it experiences a torque. This torque tends to rotate the coil about its axis of suspension in such a way that the magnetic flux passing through the coil is maximum.

(i) A moving coil galvanometer is an instrument which

(ii) To make the field radial in a moving coil galvanometer

(iii) The deflection in a moving coil galvanometer is

(iv) In a moving coil galvanometer, having a coil of N-turns of area A and carrying current I is placed in a radial field of strength B.
The torque acting on the coil is

(v) To increase the current sensitivity of a moving coil galvanometer, we should decrease

A charged particle moving in a magnetic field experiences a force that is proportional to the strength of the magnetic field, the component of the velocity that is perpendicular to the magnetic field and the charge of the particle.
This force is given by \(\vec{F}=q(\vec{v} \times \vec{B})\) where q is the electric charge of the particle, v is the instantaneous velocity of the particle, and B is the magnetic field (in tesla).
The direction of force is determined by the rules of cross product of two vectors
Force is perpendicular to both velocity and magnetic field. Its direction is same as \(\vec{v} \times \vec{B}\) if q is positive and opposite of \(\vec{v} \times \vec{B}\) if q is negative
The force is always perpendicular to both the velocity of the particle and the magnetic field that created it. Because the magnetic force is always perpendicular to the motion, the magnetic field can do no work on an isolated charge. It can only do work indirectly, via the electric field generated by a changing magnetic field.

(I) When a magnetic field is applied on a stationary electron, it

(ii) A proton is projected with a uniform velocity v along the axis of a current carrying solenoid, then

(iii) A charged particle experiences magnetic force in the presence of magnetic field. Which of the following statement is correct?

(iv) A charge q moves with a velocity 2 ms^-1 along x-axis in a uniform magnetic field \(\vec{B}=(\hat{i}+2 \hat{j}+3 \hat{k}) \mathrm{T}\) then charge will experience a force

(v) Moving charge will produce