Advertisements
Advertisements
Question
A long, straight wire carrying a current of 30 A is placed in an external, uniform magnetic field of 4.0 × 10−4 T parallel to the current. Find the magnitude of the resultant magnetic field at a point 2.0 cm away from the wire.
Solution
Given:
Uniform magnetic field, B0 = 4.0 × 10−4 T
Magnitude of current, I = 30 A
Separation of the point from the wire, d = 0.02 m
Thus, the magnetic field due to current in the wire is given by
\[B = \frac{\mu_0 I}{2\pi d}\]
\[= \frac{2 \times {10}^{- 7} \times 30}{0 . 02}\]
\[ = 3 \times {10}^{- 4} T\]
B0 is perpendicular to B (as shown in the figure).
∴ Resultant magnetic field
\[B_{net} = \sqrt{B^2 + {B_0}^2}\]
\[ = \sqrt{(4 \times {10}^{- 4} )^2 + (3 \times {10}^{- 4} )^2}\]
\[ = 5 \times {10}^{- 4} T\]
APPEARS IN
RELATED QUESTIONS
Show that the kinetic energy of the particle moving in a magnetic field remains constant.
A moving charged particle q travelling along the positive x-axis enters a uniform magnetic field B.
When will the force acting on q be maximum?
A flexible wire of irregular shape, abcd, as shown in the figure, turns into a circular shape when placed in a region of magnetic field which is directed normal to the plane of the loop away from the reader. Predict the direction of the induced current in the wire.
A proton and a deuteron having equal momenta enter in a region of a uniform magnetic field at right angle to the direction of a the field. Depict their trajectories in the field.
Write the expression for the force,`vecF` acting on a charged particle of charge ‘q’, moving with a velocity `vecV` in the presence of both electric field `vecF`and magnetic field `vecB` . Obtain the condition under which the particle moves undeflected through the fields.
A beam consisting of protons and electrons moving at the same speed goes through a thin region in which there is a magnetic field perpendicular to the beam. The protons and the electrons
An electric current i enters and leaves a uniform circular wire of radius a through diametrically opposite points. A charged particle q, moving along the axis of the circular wire, passes through its centre at speed v. The magnetic force acting on the particle, when it passes through the centre, has a magnitude equal to
A particle is projected in a plane perpendicular to a uniform magnetic field. The area bounded by the path described by the particle is proportional to
A magnetic field of \[(4.0\times10^-3 \overrightarrow k)\] T exerts a force of \[(4.0 \overrightarrow i + 3.0 \overrightarrow j ) \times 10^{−10} N\] on a particle with a charge of 1.0 × 10−9 C and going in the x − y plane. Find the velocity of the particle.
An experimenter's diary reads as follows: "A charged particle is projected in a magnetic field of `(7.0 vec i - 3.0 vecj)xx 10^-3 `T. The acceleration of the particle is found to be `(x veci + 7.0 vecj )` The number to the left of i in the last expression was not readable. What can this number be?
A current of 2 A enters at the corner d of a square frame abcd of side 20 cm and leaves at the opposite corner b. A magnetic field B = 0.1 T exists in the space in a direction perpendicular to the plane of the frame, as shown in the figure. Find the magnitude and direction of the magnetic forces on the four sides of the frame.
A magnetic field of strength 1.0 T is produced by a strong electromagnet in a cylindrical region of radius 4.0 cm, as shown in the figure. A wire, carrying a current of 2.0 A, is placed perpendicular to and intersecting the axis of the cylindrical region. Find the magnitude of the force acting on the wire.
A current i is passed through a silver strip of width d and area of cross-section A. The number of free electrons per unit volume is n. (a) Find the drift velocity v of the electrons. (b) If a magnetic field B exists in the region, as shown in the figure, what is the average magnetic force on the free electrons? (c) Due to the magnetic force, the free electrons get accumulated on one side of the conductor along its length. This produces a transverse electric field in the conductor, which opposes the magnetic force on the electrons. Find the magnitude of the electric field which will stop further accumulation of electrons. (d) What will be the potential difference developed across the width of the conductor due to the electron-accumulation? The appearance of a transverse emf, when a current-carrying wire is placed in a magnetic field, is called Hall effect.
Protons with kinetic energy K emerge from an accelerator as a narrow beam. The beam is bent by a perpendicular magnetic field, so that it just misses a plane target kept at a distance l in front of the accelerator. Find the magnetic field.
A narrow beam of singly charged potassium ions of kinetic energy 32 keV is injected into a region of width 1.00 cm with a magnetic field of strength 0.500 T, as shown in the figure. The ions are collected at a screen 95.5 cm away from the field region. If the beam contains isotopes of atomic weights 39 and 41, find the separation between the points where these isotopes strike the screen. Take the mass of a potassium ion = A (1.6 × 10−27) kg, where A is the mass number.
A particle moves in a circle of diameter 1.0 cm under the action of a magnetic field of 0.40 T. An electric field of 200 V m−1 makes the path straight. Find the charge/mass ratio of the particle.
A particle with a charge of 5.0 µC and a mass of 5.0 × 10−12 kg is projected with a speed of 1.0 km s−1 in a magnetic field of magnitude 5.0 mT. The angle between the magnetic field and the velocity is sin−1 (0.90). Show that the path of the particle will be a helix. Find the diameter of the helix and its pitch.
A uniform magnetic field of 1.5 T exists in a cylindrical region of radius 10.0 cm, its direction parallel to the axis along east to west. A wire carrying current of 7.0 A in the north to south direction passes through this region. What is the magnitude and direction of the force on the wire if,
(a) the wire intersects the axis,
(b) the wire is turned from N-S to northeast-northwest direction,
(c) the wire in the N-S direction is lowered from the axis by a distance of 6.0 cm?
A particle of mass 10 mg and having a charge of 50 mC is projected with a speed of 15 m/s into a uniform magnetic field of 125 mT. Assuming that the particle is projected with its velocity perpendicular to the magnetic field, the time after which the particle reaches its original position for the first time is ______.
