Magnetic Effect of Current

A solenoid of 1000 turns per metre has a core with relative permeability 500. Insulated windings of the solenoid carry an electric current of 5A. The magnetic flux density produced by the solenoid is : (permeability of free space = 4\(\pi\)...

A hairpin like shape as shown in figure is made by bending a long current carrying wire. What is the magnitude of a magnetic field at point P which lies on the centre of the semicircle?

A charge Q is moving \(\overrightarrow {dl}\) distance in the magnetic field \(\overrightarrow {B}\). Find the value of work done by \(\overrightarrow {B}\).

A long, straight wire of radius a carries a current
distributed uniformly over its cross-section. The
ratio of the magnetic fields due to the wire at
distance
\({a \over 3}\)
and 2\(a\), respectively from the axis
of the wire is :

A charged particle of mass 'm' and charge 'q'
moving under the influence of uniform electric
field \(E\overrightarrow i\)
and a uniform magnetic field \(B\overrightarrow k\)
follows a trajectory from point P to Q as shown
in figure. The v...

A small circular loop of conducting wire has
radius a and carries current I. It is placed in a
uniform magnetic field B perpendicular to its
plane such that when rotated slightly about its
diameter and released, it starts performing
simple ...

An electron gun is placed inside a long solenoid
of radius R on its axis. The solenoid has n
turns/length and carries a current I. The
electron gun shoots an electron along the radius
of the solenoid with speed v. If the electron
does not h...

Photon with kinetic energy of 1MeV moves
from south to north. It gets an acceleration of
1012 m/s2 by an applied magnetic field (west to
east). The value of magnetic field : (Rest mass
of proton is 1.6 × 10–27 kg) :

A very long wire ABDMNDC is shown in
figure carrying current I. AB and BC parts are
straight, long and at right angle. At D wire
forms a circular turn DMND of radius R. AB,
BC parts are tangential to circular turn at N and
D. Magnetic field...

A particle of mass m and charge q has an initial velocity \(\overrightarrow v = {v_0}\widehat j\)
. If an electric field \(\overrightarrow E = {E_0}\widehat i\)
and
magnetic field \(\overrightarrow B = {B_0}\widehat i\)
act on the part...

A particle of charge q and mass m is moving with a velocity \(- v\widehat i\) (v \(\ne\) 0) towards a large screen
placed in the Y - Z plane at a distance d. If there is a magnetic field \(\overrightarrow B = {B_0}\widehat k\)
, the max...

An electron is moving along +x direction with a velocity of 6 \(\times\) 106
ms–1. It enters a region of uniform
electric field of 300 V/cm pointing along +y direction. The magnitude and direction of the magnetic
field set up in this reg...

A square loop of side 2\(a\) and carrying current I is kept in xz plane with its centre at origin. A long
wire carrying the same current I is placed parallel to z-axis and passing through point (0, b, 0),
(b >> a). The magnitude of torque o...

A charged particle going around in a circle can be considered to be a current loop. A particle of
mass m carrying charge q is moving in a plane with speed v under the influence of magnetic field \(\overrightarrow B\).
The magnetic moment o...

A square loop of side 2\(a\), and carrying current
I, is kept in XZ plane with its centre at origin.
A long wire carrying the same current I is
placed parallel to the z-axis and passing
through the point (0, b, 0), (b >> a). The
magnitude o...

An iron rod of volume 10–3 m3 and relative
permeability 1000 is placed as core in a
solenoid with 10 turns/cm. If a current of 0.5 A
is passed through the solenoid, then the
magnetic moment of the rod will be :

A wire A, bent in the shape of an arc of a circle, carrying a current of 2 A and having radius 2 cm and another wire B, also bent in the shape of arc of a circle, carrying a current of 3 A and having radius of 4 cm, are placed as shown in t...

A circular coil has moment of inertia 0.8 kg m2
around any diameter and is carrying current to
produce a magnetic moment of 20 Am2
. The coil is kept initially in a vertical position and it can
rotate freely around a horizontal diameter. W...

A charged particle carrying charge 1 \(\mu\)C is moving with velocity \(\left( {2\widehat i + 3\widehat j + 4\widehat k} \right)\) ms–1. If an external
magnetic field of \(\left( {5\widehat i + 3\widehat j - 6\widehat k} \right)\)× 10–3 T ...

Magnitude of magnetic field (in SI units) at the
centre of a hexagonal shape coil of side 10 cm,
50 turns and carrying current I (Ampere) in
units of \({{{\mu _0}I} \over \pi }\) is :

A galvanometer coil has 500 turns and each turn has an average area of 3 \(\times\) 10–4 m2
. If a torque of
1.5 Nm is required to keep this coil parallel to a magnetic field when a current of 0.5 A is flowing
through it, the strength of ...

A beam of protons with speed 4 × 105 ms–1
enters a uniform magnetic field of 0.3 T at an
angle of 60° to the magnetic field. The pitch of
the resulting helical path of protons is close to :
(Mass of the proton = 1.67 \(\times\) 10–27 kg, ...

The figure shows a region of length ‘l’ with a
uniform magnetic field of 0.3 T in it and a
proton entering the region with velocity 4 \(\times\) 105
ms–1 making an angle 60o with the field. If the
proton completes 10 revolution by the tim...

A wire carrying current I is bent in the shape
ABCDEFA as shown, where rectangle ABCDA
and ADEFA are perpendicular to each other. If
the sides of the rectangles are of lengths a and
b, then the magnitude and direction of
magnetic moment of ...

An infinitely long current carrying wire and a small current carrying loop are in the plane of the paper as shown. The radius of the loop is a and distance of its centre from the wire is d (d > > a). If the loop a applies a force F on the...

A current loop, having two circular arcs joined by two radial lines is shown in the figure. It carries a current of 10 A. The magnetic field at point O will be close to :

One of the two identical conducting wires of length L is bent in the form of a circular loop and the other one into a circular coil of N identical turns. If the same current is passed in both, the radio of the magnetic field at the central ...

A particle having the same charge as of electron moves in a ciurcular path of radius 0.5 cm under the influence of a magnetic field 0f 0.5 T. If an electric field of 100 V/m makes it to move in a straight path, then the mass of the particle...

A rigid square loop of side 'a' and carrying
current I2 is lying on a horizontal surface near
a long current I1 carrying wire in the same plane
as shown in figure. The net force on the loop
due to wire will be :

A rectangular coil (Dimension 5 cm × 2.5 cm)
with 100 turns, carrying a current of 3 A in the
clock-wise direction is kept centered at the
origin and in the X-Z plane. A magnetic field
of 1 T is applied along X-axis. If the coil is tilted
t...

A moving coil galvanometer has a coil with
175 turns and area 1 cm2. It uses a torsion band
of torsion constant 10–6 N-m/rad. The coil is
placed in a maganetic field B parallel to its
plane. The coil deflects by 1° for a current of
1 mA. Th...

A thin strip 10 cm long is on a U shaped wire
of negligible resistance and it is connected to
a spring of spring constant 0.5 Nm–1
(see figure). The assembly is kept in a uniform
magnetic field of 0.1 T. If the strip is pulled

from its equ...

A circular coil having N turns and radius r
carries a current I. It is held in the XZ plane in
a magnetic field B\({\mathop i\limits^ \wedge }\) . The torque on the coil due
to the magnetic field is :

Two very long, straight, and insulated wires are
kept at 90° angle from each other in xy-plane
as shown in the figure. These wires carry
currents of equal magnitude I, whose directions
are shown in the figure. The net magnetic field
at poin...

A proton and an \(\alpha\)-particle (with their masses in the ratio of 1 : 4 and charges in the ratio of 1 : 2) are accelerated from rest through a potential difference V. If a uniform magnetic field (B) is set up perpendicular to their ve...

As shown in the figure, two infinitely long, identical wires are bent by 90o and placed in such a way that the segments LP and QM are along the x-axis, while segments PS and QN are parallel to the y-axis. If OP = OQ = 4cm, and the magnitude...

A thin ring of 10 cm radius carries a uniformly distributed charge. The ring rotates at a constant angular
speed of 40 \(\pi\) rad s–1
about its axis, perpendicular to its plane. If the magnetic field at its centre is 3.8 × 10–9
T, then t...

Find the magnetic field at point P due to a straight line segment AB of length 6 cm carrying a current of 5A.
(See figure) (\(\mu\)0 = 4\(\pi\) × 10–7 N-A–2)

An electron, moving along the x-axis with an initial energy of 100 eV, enters a region of magnetic field \(\overrightarrow B = \left( {1.5 \times {{10}^{ - 3}}T} \right)\widehat k\)
at S (See figure). The field extends between x = 0 and x...

In an experiment, electrons are accelerated, from rest, by applying a voltage of 500 V. Calculate the radius of the path if a magnetic field 100 mT is then applied. [Charge of the electron = 1.6 \(\times\) 10–19 C Mass of the electron = 9...

The region between y = 0 and y = d contains a magnetic field \(\overrightarrow B = B\widehat z\). A particle of mass m and charge q enters the region with a velocity \(\overrightarrow v = v\widehat i.\) If d \(=\) \({{mv} \over {2qB}},\)...

A particle of mass m and charge q is in an electric and magnetic field given by
\(\overrightarrow E = 2\widehat i + 3\widehat j;\,\,\,\overrightarrow B = 4\widehat j + 6\widehat k.\)
The charged particle is shifted from he origin to the p...

An insulating thin rod of length \(l\) has a linear charge density \(\rho \left( x \right)\) = \({\rho _0}{x \over l}\) on it. The rod is rotated about an axis passing through the origin (x = 0) and perpendicular to the rod. If the rod make...

A hoop and a solid cylinder of same mass and radius are made of a permanent magnetic material with their magnetic moment parallel to their respective axes. But the magnetic moment of hoop is twice of solid cylinder. They are placed in a uni...

A proton, an electron, and a Helium nucleus,
have the same energy. They are in circular
orbits in a plane due to magnetic field
perpendicualr to the plane. Let rp, re and rHe be
their respective radii, then

Two wires A & B are carrying currents I1 & I2
as shown in the figure. The separation between
them is d. A third wire C carrying a current I
is to be kept parallel to them at a distance x from
A such that the net force acting on it is zero.
...

The magnitude of the magnetic field at the centre of an equilateral triangular loop of side 1 m which is
carrying a current of 10 A is : [Take \(\mu\)0 = 4\(\pi\) × 10–7
NA–2]

A square loop is carrying a steady current I and the magnitude of its magnetic dipole moment is m. if this
square loop is changed to a circular loop and it carries the same current, the magnitude of the magnetic dipole
moment of circular lo...

A charge q is spread uniformly over an insulated loop of radius r. If it is rotated with an angular velocity \(\omega\) with resect to normal axis then the magnetic moment of the loop is :

A Helmholtz coil has a pair of loops, each with \(N\) turns and radius \(R\). They are placed coaxially at distance \(R\) and the same current \({\rm I}\) flows through the loops in the same direction. \(P,\) midway between the centers $$A$...