Magnetic Field Strength Around a Wire

From the demonstration, we saw that: the magnetic field strength varies directly with the amount of current flowing through the wire i.e. B  I the magnetic field strength varies inversely with the distance from the wire. i.e.

Thus we combine these together to get as an equation for mathematical & historical reasons the constant k has been written as

however we shall for simplicity use "k“ Our formula then is where B = magnetic field strength (Tesla) I = current (Amps) r = distance from wire (m) k = permeability of free space constant = 2 x 10 -7

Sample: A vertical wire carries a current of 25.0 A. What is the magnetic field strength 15 cm from the wire?

Magnetic Field Strength inside a Loop We predict the field strength will be greater inside a loop. There are wires all around the region exerting a magnetic field. The lines of flux reinforce each other. The formula for a single loop is r = radius of coil

For a coil, the strength depends on the number of coils. (N)

Sample: If the magnetic field strength at the centre of a loop of 12 coils is 4.00 x T, and the radius is 12.0 cm, find the current that is flowing,

Magnetic Field Strength inside a Solenoid The formula for magnetic field strength inside a solenoid is B = 2  knI where n = number of turns / m

Sample: A 10 cm long solenoid has 400 turns of wire and carries a current of 2.00 A. Calculate the magnetic field strength inside the solenoid. n = 400 turns / 0.1m = 4000 / m B = 2  knI B = 2  2 x (4000)(2) B=1.0 x T