Question

Scientists in a lab with very large windows create an electric and magnetic field which they observe as

E = (400 i - 100 j) N / C
B = (0.8 j + 0.2 k) T
Another scientist travels past the lab in a rocket sled. As she passes, she looks through the windows and measures the electric and magnetic fields. If the sled's velocity is 2780 i m/s , what magnetic field does she observe? Give your answer as an overall magnitude in Tesla.

Answer 1

The magnetic field observed by the scientist traveling past the lab is 0.800421 T.

Step-by-step explanation:

When the scientist traveling past the lab measures the electric and magnetic fields, the magnetic field observed depends on the relative velocity of the sled and the lab. To find the magnetic field observed, we can use the equation:

B' = B - (v x E / c^2)

Substituting the values:

B' = (0.8 j + 0.2 k) T - (2780 i m/s x (400 i - 100 j) N / C) / (3 x 10^8 m/s)^2

Calculating the cross product and simplifying, we find that the overall magnitude of the magnetic field observed is 0.800421 T.