Question

An electron has velocity V = (2×10^6ms^-1)i cap+(3×10^6ms^-1)j cap.Magnetic field present in the region is B = 0.03Ti cap-0.15Tj cap. The force on the electron is:
a)(6.24×10^-14N)k cap
b)(3.56×10^-14N)k cap
c)(8×10^14N)k cap
d)(6.24×10^14N)k cap.​

Answer 1

d is the correct one please mark me as brainlist

Answer 2

Option (A) is correct

Explanation: As per Lorentz Force equation, Force on the electron ( ) = \vec{v} x \vec{B}  

Where \vec{v} is the velocity vector of electron

           \vec{B} is Magnetic Field Vector in the region / vicinity of electron.

Substitute respective values of the parameters in the Lorentz Force Equation and do vector cross multiplication:

= -1.6 x 10-19 [{(2x106)\hat{i}+ (3x106)\hat{j}} x {0.03\hat{i} – 0.15\ \hat{j}}]

                 = -1.6 x 10-13 [{2\hat{i} + 3\ \hat{j}} x {0.03\hat{i} – 0.15\ \hat{j}}]  

                 = -1.6x10-13 [{-0.3\ \hat{k} - 0.09\hat{k}}] = +0.624x10-13\hat{k} N = 6.24x10-14\hat{k} N