If the EMF produced in a wire is 0.88 volts and the wire moves perpendicular to a magnetic field of strength 0.075 newtons/amp·meter at a speed of 4.20 meters/second, what is the length of the wire in the magnetic field?

Use the formula

E.M.F. = L*B*V , where

B = 0.075 Tesla (or N/amp*m)
EMF = 0.88 Volts
V = 4.2 m/s
Solve for L

L = 2.8 m

To find the length of the wire in the magnetic field, we can use the formula for induced electromotive force (EMF):

EMF = B * v * L

Where:
EMF is the induced electromotive force
B is the magnetic field strength
v is the velocity of the wire
L is the length of the wire in the magnetic field

Rearranging the formula, we get:

L = EMF / (B * v)

Plugging in the given values:

EMF = 0.88 volts
B = 0.075 newtons/amp·meter
v = 4.20 meters/second

L = 0.88 / (0.075 * 4.20)

Calculating the result:

L = 0.88 / 0.315

L ≈ 2.793 meter (rounded to three decimal places)

Therefore, the length of the wire in the magnetic field is approximately 2.793 meters.

To find the length of the wire in the magnetic field, we can use the formula for the electromotive force (EMF) induced in a wire moving perpendicularly through a magnetic field:

EMF = B * L * v

Where:
EMF is the electromotive force (in volts)
B is the magnetic field strength (in teslas or weber/m^2)
L is the length of the wire in the magnetic field (in meters)
v is the velocity of the wire perpendicular to the magnetic field (in meters/second)

In this case, we need to rearrange the formula to solve for L:

L = EMF / (B * v)

Given:
EMF = 0.88 volts
B = 0.075 newtons/amp·meter
v = 4.20 meters/second

We substitute these values into the formula:

L = 0.88 volts / (0.075 newtons/amp·meter * 4.20 meters/second)

Now, let's simplify the equation:

L = 0.88 volts / (0.315 newtons·seconds/meter^2)

To divide by a unit, we can multiply by its reciprocal:

L = 0.88 volts * (1 meter^2 / 0.315 newtons·seconds)

L = 0.88 volts * (1 meter^2 / 0.315 newtons·seconds)

L = 2.7936 meters^2 / newtons·seconds

Finally, we can convert meters^2/newtons·seconds to meters:

L = 2.7936 meters

Therefore, the length of the wire in the magnetic field is approximately 2.7936 meters.