Q. 74.5( 4 Votes )
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.
Current in the wire : I = 30 A
External Uniform magnetic field: BO = 4.0 ×10–4 T
Distance between the point and the wire : d = 2 cm = 0.02 m
Here, B is the magnetic field due to wire. BO is parallel to the current in the wire. Using Right hand rule we can see that direction of magnetic field at the desired point is going into the plane (cross). This direction due to wire is perpendicular to the External magnetic field.
By Ampere’s Law for a current carrying wire is
Here, B is the magnitude of magnetic field, μ0 is the permeability of free space and μ0= 4π × 10-7 T mA-1 and d is the distance between the current carrying wire and the required point.
Substituting we get,
∴ B = 3× 10-4 T
As Magnetic field due to wire is perpendicular to the external magnetic field, the resultant net magnetic field would be:
∴ Bnet = 5 × 10-4 T
Hence, the magnitude of the resultant magnetic field at a point 2.0 cm away from the wire is 5 × 10-4 T.
Rate this question :
(a) An iron ring of relative permeability μr has windings of insulated copper wire of n turns per metre. When the current in the windings is I, find the expression for the magnetic field in the ring.
(b) The susceptibility of a magnetic material is 0.9853. Identify the type of magnetic material. Draw the modification of the field pattern on keeping a piece of this material in a uniform magnetic field.Physics - Board Papers
(i) Derive an expression for the magnetic field at a point on the axis of a current carrying circular loop.
(ii) A coil of 100 turns (tightly bound) and radius 10 cm. carries a current of 1A. What is the magnitude of the magnetic field at the center of the coil?
State Ampere’s circuital law. Consider a long straight wire of a circular cross section (radius a) carrying steady current I. The current I is uniformly distributed across this cross section. Using Ampere’s circuital law, find the magnetic field in the region r < a and r > a.
Physics - Exemplar
Two identical current carrying coaxial loops, carry current I in an opposite sense. A simple Amperian loop passes through both of them once. Calling the loop as C,Physics - Exemplar
Quite often, connecting wires carrying currents in opposite directions are twisted together in using electrical appliances. Explain how it avoids unwanted magnetic fields.HC Verma - Concepts of Physics Part 2
A long, straight wire carries a current. Is Ampere’s law valid for a loop that does not enclose the wire, or that encloses the wire but is not circular?HC Verma - Concepts of Physics Part 2
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?
(b) What will be the minimum magnitude of the resultant magnetic field?
HC Verma - Concepts of Physics Part 2
A current 10 A is established in a long wire along the positive z-axis. Find the magnetic filed . At the point (1m, 0, 0).