Advertisements
Advertisements
Question
A long, straight wire of radius r carries a current i and is placed horizontally in a uniform magnetic field B pointing vertically upward. The current is uniformly distributed over its cross section. (a) At what points will the resultant magnetic field have maximum magnitude? What will be the maximum magnitude? (b) What will be the minimum magnitude of the resultant magnetic field?
Advertisements
Solution
(a) As the wire in question is carrying current, so it will also generate a magnetic field around it. And for a long straight wire it will be maximum at the mid-point called P.
Now,
Magnetic field generated by the current carrying wire \[= \frac{\mu_o i}{2\pi r}\]
Net magnetic field = \[B + \frac{\mu_0 i}{2\pi r}\]
(b) Magnetic field B = 0
when \[r < \frac{\mu_0 i}{2\pi B}\]
Clearly,
B = 0
when
\[r = \frac{\mu_0 i}{2\pi B}\]
But when \[r > \frac{\mu_0 i}{2\pi B}\]
Net magnetic field = \[B - \frac{\mu_0 i}{2\pi r}\]
APPEARS IN
RELATED QUESTIONS
Using the concept of force between two infinitely long parallel current carrying conductors, define one ampere of current.
How does one understand this motional emf by invoking the Lorentz force acting on the free charge carriers of the conductor? Explain.
Two parallel, long wires carry currents i1 and i2 with i1 > i2. When the currents are in the same direction, the magnetic field at a point midway between the wires is 10 µT. If the direction of i2 is reversed, the field becomes 30 µT. The ratio i1/i2 is
A long, straight wire carries a current along the z-axis, One can find two points in the x−y plane such that
(a) the magnetic fields are equal
(b) the directions of the magnetic fields are the same
(c) the magnitudes of the magnetic fields are equal
(d) the field at one point is opposite to that at the other point.
A current of 10 A is established in a long wire along the positive z-axis. Find the magnetic field \[\vec{B}\] at the point (1 m, 0, 0).
A long, straight wire carrying a current of 1.0 A is placed horizontally in a uniform magnetic field B = 1.0 × 10−5 T pointing vertically upward figure. Find the magnitude of the resultant magnetic field at the points P and Q, both situated at a distance of 2.0 cm from the wire in the same horizontal plane.
The magnetic field existing in a region is given by `vecB = B_0(1 + x/1)veck` . A square loop of edge l and carrying a current i, is placed with its edges parallel to the x−y axes. Find the magnitude of the net magnetic force experienced by the loop.
A rectangular coil of 100 turns has length 5 cm and width 4 cm. It is placed with its plane parallel to a uniform magnetic field and a current of 2 A is sent through the coil. Find the magnitude of the magnetic field B if the torque acting on the coil is 0.2 N m−1
A straight, how wire carries a current of 20 A. Another wire carrying equal current is placed parallel to it. If the force acting on a length of 10 cm of the second wire is 2.0 × 10−5 N, what is the separation between them?
Three coplanar parallel wires, each carrying a current of 10 A along the same direction, are placed with a separation 5.0 cm between the consecutive ones. Find the magnitude of the magnetic force per unit length acting on the wires.
Answer the following question.
Two infinitely long straight wire A1 and A2 carrying currents I and 2I flowing in the same direction are kept' distance apart. Where should a third straight wire A3 carrying current 1.5 I be placed between A1 and A2 so that it experiences no net force due to A1 and A2? Does the net force acting on A3 depend on the current flowing through it?
If a current I is flowing in a straight wire parallel to x-axis and magnetic field is there in the y-axis then, ______.
The nature of parallel and anti-parallel currents are ______.
Three infinitely long parallel straight current-carrying wires A, B and C are kept at equal distance from each other as shown in the figure. The wire C experiences net force F. The net force on wire C, when the current in wire A is reversed will be ______.
Two long straight parallel conductors carrying currents I1 and I2 are separated by a distance d. If the currents are flowing in the same direction, show how the magnetic field produced by one exerts an attractive force on the other. Obtain the expression for this force and hence define 1 ampere.
Beams of electrons and protons move parallel to each other in the same direction. They ______.
Two long parallel wires kept 2 m apart carry 3A current each, in the same direction. The force per unit length on one wire due to the other is ______.
Two long straight parallel current-carrying conductors are kept ‘a’ distant apart in the air. The direction of current in both the conductors is the same. Find the magnitude of force per unit length and the direction of the force between them. Hence define one ampere.
