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The motion of photons, neutral and charged particles around wormhole described by exponential metric which is the solution of the Einstein-scalar field equations has been studied. It is also proven that the wormhole solution is a special case of the well-known JNW spacetime and that the scalar field corresponds to the phantom field which has the anti-gravitating repulsive feature. It is also shown that the characteristic radii, namely, innermost stable circular orbit (ISCO), marginally bound orbit (MBO) and photon sphere in the spacetime described by exponential metric are less than that obtained in the Schwarzschild spacetime. However, the size of the shadow of the wormhole is greater than the shadow of the Schwarzschild black hole. The energy efficiency in the spacetime described by exponential metric is relatively large than that in the Schwarzschild spacetime. Later it is assumed that the wormhole is embedded in the asymptotically uniform magnetic field which behaves similar to the dipole-like field near the origin. The dynamical motion of charged particles around the wormhole described by exponential metric implanted in the asymptotically uniform magnetic field has been studied assuming that charged particles are acted by gravitational and Lorentz forces, simultaneously. It is shown that the ISCO position for charged particle will be always less than that of neutral particle.