Advertisements
Advertisements
Question
Two long straight parallel conductors 'a' and 'b', carrying steady currents Ia and Ib are separated by a distance d. Write the magnitude and direction of the magnetic field produced by the conductor 'a' at the points along the conductor 'b'. If the currents are flowing in the same direction, what is the nature and magnitude of the force between the two conductors?
Advertisements
Solution
Let a and b be long straight parallel conductors. Ia and Ib are the current flowing through them and are separated by a distance d.
Magnetic field induction at a point P on a conductor b due to current Ia passing through a is
\[B_1 = \frac{\mu_0 2 I_a}{4\pi d}\]
Now, unit length of b will experience a force as
\[F_2 = B_1 I_b \times 1 = B_1 I_b \]
\[ \therefore F_2 = \frac{\mu_0}{4\pi}\frac{2 I_a I_b}{d}\]
Conductor a also experiences the same amount of force, directed towards b. Hence, a and b attract each other.
RELATED QUESTIONS
An electron beam projected along the positive x-axis deflects along the positive y-axis. If this deflection is caused by a magnetic field, what is the direction of the field? Can we conclude that the field is parallel to the z-axis?
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 copper wire of diameter 1.6 mm carries a current of 20 A. Find the maximum magnitude of the magnetic field `vecB` due to this current.
Four long, straight wires, each carrying a current of 5.0 A, are placed in a plane as shown in figure. The points of intersection form a square of side 5.0 cm.
(a) Find the magnetic field at the centre P of the square.
(b) Q1, Q2, Q3, and Q4, are points situated on the diagonals of the square and at a distance from P that is equal to the diagonal of the square. Find the magnetic fields at these points.
Two parallel wires separated by a distance of 10 cm carry currents of 10 A and 40 A along the same direction. Where should a third current by placed so that it experiences no magnetic force?
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?
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.
When two long, straight, current-carrying conductors are placed parallel to each other and the currents flow in the same direction, the conductors:
By symmetry, the magnetic field of conductor b exerts a force on conductor a. The relationship between the two forces Fba and Fab is:
