A uniform magnetic field of magnitude 0.80 T in the negative z-direction is present in a region of space,as shown in the figure.A uniform electric field is also present.An electron that is projected with an initial velocity in the positive x-direction passes through the region without deflection.What is the electric field vector in the region?
A) -73 kV/m
B) +73 kV/m
C) +110 kV/m
D) +110 kV/m
E) -110 kV/m

Question

A uniform magnetic field of magnitude 0.80 T in the negative z-direction is present in a region of space,as shown in the figure.A uniform electric field is also present.An electron that is projected with an initial velocity  in the positive x-direction passes through the region without deflection.What is the electric field vector in the region? 
A) -73 kV/m 
B) +73 kV/m 
C) +110 kV/m 
D) +110 kV/m 
E) -110 kV/m

Quizplus · Accepted Answer

Since the electron travels without deflection, the magnetic force on it (given by F=qvB) must be equal and opposite to the electric force (given by F=qE). Solving for the electric field, we get E=Bv. Substituting the given values (B=0.80 T and v=1.1x10^7 m/s), we get E=0.80x1.1x10^7=8.8x10^6 V/m. Since the electron is moving in the +x direction, the electric field must be in the -y direction (to cancel the magnetic force in the -z direction). Therefore, the electric field vector is (-8.8x10^6)j. Converting to kilovolts per meter, we get -73 kV/m. Therefore, the correct choice is A.

A Uniform Magnetic Field of Magnitude 0