9303753286127016 A circular coil carrying a current I has radius R and number of turns N . If all the three, i.e., the current I, radius R and number of turns N are doubled, then magnetic field at its centre becomes

A circular coil carrying a current I has radius R and number of turns N . If all the three, i.e., the current I, radius R and number of turns N are doubled, then magnetic field at its centre becomes

 When current I flows in a circular coil with radius R and number of turns N, we first apply the Biot-Savart law to calculate the relationship between magnetic field, radius, current, and number of turns, i.e.

We know that at the axis of a current carrying coil at distance x from the centre, magnetic field B is given by

B=μ0NIR2/2(R2+x2)3/2

At centre x=0 So,

BC=μ0NIR2/2(R2)3/2

BC=μ0NIR2/2R3

⟹ BC = μ0IN/2R …..(1)

If I, R & N are doubled then magnetic field at centre will be BC′ = μ0(2I)(2N)/2(2R)

⟹BC′ = 2(μ0NI/2R)

From equation (1) BC′ = 2BC

Hence, the magnetic field at the centre will also become doubled.

Balkishan Agrawal

At the helm of GMS Learning is Principal Balkishan Agrawal, a dedicated and experienced educationist. Under his able guidance, our school has flourished academically and has achieved remarkable milestones in various fields. Principal Agrawal’s vision for the school is centered on providing a nurturing environment where every student can thrive, learn, and grow.

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