Home
Class 12
PHYSICS
Two identical coils P & Q each of radius...

Two identical coils P & Q each of radius R are lying in perpendicular planes such that they have a common centre. Find the magnitude and direction of magnetic field at the common centre of the two coils, if they currents equal to I and `sqrt2` I respectively.

Text Solution

Verified by Experts

Two coils are lying in perpendicular planes and having common centre .
The current carrying by P and Q is I and `sqrt2` I .
The magnetic field at the centre of P due, to its current I .

`vecB_(p) = (mu_(0)I)/(2 R) `
Magnetic field at centre of Q , due to its current `sqrt2` I.
`vecB_(Q) = (mu_(0)sqrt2I)/(2 R) `
` :. vecB_("net") = vecB_(p) + vecB_(Q) `
` = (mu_(0)I)/(2R) + (mu_(0)sqrt2 I)/(2 R) `
`|vecB_("net")| = sqrt(((mu_(0)I)/(2R))^(2)+((mu_(0)sqrt2I)/(2R))^(2))`
` = (mu_(0)I)/(2 R) xx 2 = (mu_(0)I)/R`
` :. tan theta = (|vecB_(p)|)/(|vecB_(Q)|) = R/((mu_(0)sqrt2 I)/(2R))`
` tan theta = 1/sqrt2`
` theta_(2) tan^(-1) (1/sqrt2)`
` theta = 31^(@)`
Promotional Banner

Similar Questions

Explore conceptually related problems

Two circular coils of radii 5.0 cm and 10 cm carry equal currents of 2.0 A. The coils have 50 and 100 turns respectively and are placed in such a way that their planes as well as the centres coincide. Find the magnitude of the magnetic field B at the common centre of the coils if the currents in the coils are (a) in the same sense (b) in the opposite sense.

Consider a tightly wound 100 turn coil of radius 10 cm, carrying a current of 1 A. What is the magnitude of the magnetic field at the centre of the coil?

Two similar coils of radius R are lying concentrically with their planes at right angles to each other. The currents flowing on them are I and 2I, respectively. The resultant magnetic field induction at the centre will be:

A circular coil of 120 turns has a radius of 18 cm and carries a current of 3 A. What is the magnitude of the magnetic field at a point on the axis of the coil at a distance from the centre equal to the radius of the circular coil .

A cirular coil of wire cansiting of 100 turns ,each of readius 8.0 cm carries a current of 0.40 A. What is the magnitude of the magnetic field barB at the centre of the coil ?

Two idential coil of 5 turns each carry 1 A and 2 A current respectively. Assume they have common centre with their planes to each other. If their radius is 1 m each and direction of flow of current in the coils are in opposite directions, then the magnetic field produced on its axial line at a distance of sqrt(3) m from the common centre is (in tesla)

What is the current passing through a coil of radius of 8 cm having 50 turns, when a magnetic field at the centre of the coil is 1.57xx10^(-6) T ?

A circular loop of radius r carries a current i. where should a long , straight wire carrying a current 4i be placed in the plane of the circle so that the magnetic field at the centre becomes zero?

Calculate the current passing through a coil of diameter 20 cm , having 50 turns, when the magnetic field at the centre of the coil is 2.5xx10^(-6) T .