A proton moves with a velocity of 5 10^6 j ms ⁻¹ through the uniform electric field, E =4 10^6[2 i +0.2 j +0.1 k ] Vm ⁻¹ and the uniform magnetic field B =0.2 i +0.2 j + k ] T . The approximate net force acting on the proton is

Step-by-step solution

Given, speed of proton, v=5 10^6 j m / s Electric field, E =4 10^6[2 i +0.2 j +0.1 k ] V / m Magnetic field, B =0.2[ i +0.2 j + k ] T Charge on proton, q=1.6 10⁻¹⁹ C Net force acting on the proton is calculated according to Lorentz's force as aligned & F =q[ E + v B ] & =1.6 10⁻¹⁹ [4 10^6(2 i +0.2 j +0.1 k ) . & .+5 10^6 j 0.2( i +0.2 j + k ) ] & =1.6 10⁻¹⁹ 10^6[4(2 i +0.2 j +0.1 k ) & +(- k +0+5 i )] & F =1.6 10⁻¹³[13 i +0.8 j -0.6 k ] & F =| F |=1.6 10⁻¹³ (13)^2+(0.8)^2+(0.6)^2 & =1.6 10⁻¹³ 170 =20.86 10⁻¹³ ~N &