Question

Ampere's Law for a long wire states that magnetic field is directly proportional to current and inversely proportional to the distance for the wire. True or False.

Ampere's Law for a loop wire states that magnetic field is indirectly proportional to current and directly proportional to the radius of the loop. True or False.

Ohm's Law is true regardless of the nature of the electric circuit. True or False

Thank you!

Answer 1

1) for the first case it is true

illustration

let us consider two long parallel conductors P and Q in the form of a wire separated by a distance 'd' and carrying currents I1 and I2. The conductor P will produce a magnetic field at all points around it.

The magnetic field B1 due to the condusctor P at the site of the conductor Q is given by

B1 =(0 / 4)(2I1 / d^2)-------(1)

here in eqn (1)

0 /4 is a constant and so it can be said that

the magnetic field is directly proportional to the current I and inversely proportional to the distance d.

2)For the second case it is false

illustration

The magnetic field on the axis of a circular loop of radius R carrying a current I has a mag2nitude

B = (0 /4) (2IR^2) / (R^2 +x ^2)^3/2-------(2)

here the magnetic field of a loop is directly proportional to the product of the current and square of the resistance.

here again (0/4) is a constant

here x is the distance along the axis from the centre of the loop.For x >> R, we can neglect R^2 when compared to x^2 in the denomonator.then eqn(2) becomes

B = (0 / 4) (2IR^2 / x^3)------(3)

here area A = R^2

SUBSTITUTING FOR AREA IN EQN (3) WE GET

B =( 0 / 4) ( 2IA/x^3)

3)for the third case it is false

Ohm's law depends on the nature of the circuit

we have the eqn R =  V / I

according to this law the current flowing through the circuit is directly proportional to the potential difference v across the two ends of the conductor provided the temperature and other physical conditions remains the same.

here I is proportional to the voltage V

THE CIRCUIT MAINLY DEPENDS ON THE POTENTIAL DIFFERENCE AND THE RESPECTIVE CURRENT WHICH FLOWS.